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mm. The surfaces of both the dogbone and the pads were ground, and the surface roughness is characterised by Ra=313 |
nm across the grinding direction and Ra=54 |
nm along the grinding direction, which also corresponds to the walking direction. The results to be described should be read in conjunction with , where the upper points are the coefficient of friction, to be read with the left hand scale and the broken line is the accumulated distance walked, to be read off the right hand scale. The loads (given in kN) annotated on the broken line are the tangential force, Q. The walking distance per cycle, Δs, was measured using a standard LVDT mounted on a pad assembly of the kind shown in The tangential force was set to a constant value (initially low) and the bulk force in the dogbone was ramped up to 40.4 |
kN and set oscillating between the values 0.4 |
kN and 40.4 |
kN at the frequency of 1Hz. The test was continued but, approximately every fifty cycles, the tangential load was increased until walking was detected: thus the first 387 cycles were used up with the pads stationary. At this point the shearing force had been increased to 0.8 |
kN, and some movement of the pads was detected. Subsequently, small increases in the value of the shear force were applied until, by cycle 897, a shear force of 1 |
kN was reached and, from the walking distance measured, we infer a coefficient of friction, at this point, of about 0.83. Over the next 10 cycles the distance walked per cycle fell slightly, as the coefficient of friction increased. As an experiment, at this point the shearing force was reduced to 0.9 |
kN, whereupon walking stopped. At cycle 1325 the shearing force was restored to the value of 1.0 |
kN and walking resumed, but the pace length reduced further, indicating a another small increase in the coefficient of friction, to about 0.865. At cycle 1500 the shearing force was increased to 1.1 |
kN permitting the pad to take ‘a pace’, and reducing it back to 1.0 |
kN caused walking to cease. Further increases in the shearing force to 1.1 |
kN and subsequently 1.2 |
kN were imposed and the walking length increases significantly, whilst the coefficient of friction fell very slightly (from a maximum of 0.867 to about 0.85). We believe that this was because key parts of the contact were now moving onto less heavily modified material. It should be noted here that the values of coefficient of friction obtained using the newly developed technique compare well with those resulting form fully sliding tests carried out imposing a sliding distance of 1 |
mm per cycle, and which produced values of coefficient of friction ranging between 0.7 and 0.83 (note that it is very hard to justify quoting coefficients of friction to more than one significant figure in a conventional sliding test, because of the variability experienced during the test).As has been stated, the walking ‘rate’ is a strong function of the coefficient of friction, and so this test is a precise tool for measuring its value. In the present experiment the maximum walking distance per cycle, and therefore the maximum slip distance exhibited, was 0.85 |
μm. It follows that, in order for the contact to move by a rigid body displacement equal to one contact patch width a total of 490 cycles must be made. Also, the contact pressure present during the scrubbing motion is known, and this gives a quantitative idea of the amount of surface damage inflicted.In due course it is hoped to evolve the experimental procedure to enable the influence of contact pressure and number of cycles of load on the coefficient of friction to be found explicitly and systematically. This seems feasible because the problem is wholly controlled by elastic stress, strains and displacement, and hence these are known accurately without the need for external transducers.The test described seems a viable method of measuring, with precision, the coefficient of friction between solids. Modest changes in the load range cause sufficient change in the walking distance for the coefficient of friction, at least on aggregate, to be quoted to two significant figures with confidence. The test does not cause the amount of surface damage we usually associate with sliding A nonlocal plate model incorporating interatomic potentials for vibrations of graphene with arbitrary edge conditionsThis article presents analytical explicit frequency expressions for investigating the vibrations of single-layer graphene sheets (SLGSs). The interatomic potential is incorporated into a nonlocal continuum plate model through establishing a linkage between the strain energy density induced in the continuum and nonlocal plate constitutive relations. The model which is independent of scattered value of Young's modulus is then applied and explicit frequency formulas for the SLGSs with different edge conditions are derived using static deflection function of the nanoplate under uniformly distributed load. The reliability of the present formulation is verified by the results obtained by the molecular dynamics (MD) simulations and other research workers. The formulas are of a simple short form enabling quick and accurate evaluation of the frequency of the SLGSs and also simple calibration of scale coefficient by the use of MD simulations results.Among the various forms of carbon-based nanostructured materials graphene sheet (GS) is of great significance such that it is known as the mother of these nanostructures. The cause for such an importance lies in that most of carbon nanostructures are viewed to be constituted of GS which is being deformed into the different shapes of them such as fullerenes The modeling of nanostructured materials is carried out based on two kinds of approaches namely atomistic methods and continuum mechanics. The former which includes the methods such as molecular mechanics simulations, traditional molecular dynamics, tight-binding molecular dynamics and density functional theory Knowledge of the vibration response of the GSs which is a significant issue from design point of view has been a major concern for the research workers in this area. Behfar and Naghdabadi Accurate simple formulation plays a crucial role in description of the mechanical behavior of the structures due to its simplicity leading to the quick prediction of the response of them. In this respect, a few research workers presented a proportion of approximate formulas for the frequency and buckling load of elastic plates and nanoplates. Using static deflection of the plate, Jones Based on the literature review one can find that there is a deficiency in the analytical expressions which have been ever developed for the vibrations of GSs. In the existing continuum models, the frequency expression is dependent on the exact value of Young's modulus which is scattered in the literature and a large variation of it is reported, from 0.40 to 4.15 TPa with an average of 1.8 TPa Motivated by these considerations, the main goal of this paper is to derive independent-Young's modulus explicit expressions for the frequency of the monolayer graphene sheets with various edge supports. In this paper, the elastic material properties are directly obtained from the interatomic potential and no fitting of Young's modulus is required. To achieve this, a linkage between the strain energy density induced in the continuum and the nonlocal plate constitutive relations is established to develop a nonlocal atomistic-based plate theory for studying the vibration of the SLGSs. The static deflection of the GS under uniformly distributed loads is first considered and the governing equation is then solved by applying the Galerkin method. Comparisons between the present results and those of MD simulations and the literature are made to assess the efficiency of the present formulas. The simplicity and accuracy of the current expressions makes them an efficient tool for calculating proper value of the nonlocal parameter using MD simulations results.The Tersoff-Brenner interatomic potential function is adopted in the present continuum theory which takes the form where rij is the distance between atoms i and j. VR and VA are the pair-additive terms representing the interatomic repulsive and attractive interactions and are given bywhere De = 6 ev, S = 1.22, β = 21 nm−1, R(e) = 0.1390 nm fc(r)={1,r<R(1),12{1+cos[π(r−R(1))R(2)−R(1)]}.R1<r<R(2),0,r>R(2),where R(1) and R(2) are cutoff as 0.17 nm and 0.2 nm, respectively. The parameter Bij indicates a multi-body coupling emanating from the interaction between atoms i, j and their local environment given bywhere a0 = 0.00020813, c0 = 330, d0 = 3.5 A graphene sheet has hexagonal atomic structure, as shown in . The interatomic potential energy is at its minimum when the lattice is in equilibrium. Thus, the equilibrium length of bond, l(0), can be determined by minimizing the interatomic potential asFrom the preceding equation, one can obtain the following analytical expression for the equilibrium bond lengthwhere B0 denotes the multi-body coupling term Bij which is being calculated at the unstrained equilibrium state as 0.945 for the values of the parameters given above. Substitution of the values of B0 and the parameters R(e), β and S into Eq. gives r0 = 0.142 which is in a good agreement with the well-known equilibrium bond length of graphite (0.144 nm).In contrast to molecular dynamic simulations in which the motion of each atom is tracked, the atomistic based continuum model developed herein relates the collective behavior of atoms to continuum deformation measures of the material. This is accomplished by the Cauchy-Born rule In this article we adopt the approach of Zhang et al. . The Cauchy-Born rule also demonstrates that a homogeneous deformation transfers the atoms from the undeformed to deformed configurations according to a single mapping specified by the deformation gradient F of a material point. The bond between atoms i and j prior to deformation is described by a vector rij(0)=r0nij(0). nij(0) denotes the bond orientation prior to deformation and is given by nij(0)=cosφex+sinφey, where ex and ey are the unit vectors in the x and y direction, respectively. The vector rij becomes F·rij(0) on the deformed graphene sheet and its current length is given bywhere E=12(FT·F−I) is the Lagrangian strain and I is the second-order identity tensor.The bond density function is determined from the equality of the bond density of the graphite and the substitution media aswhere Nb denotes the number of the bonds within a cell at a material point and Ωc is the area of that cell. The cell is one of the hexagonal lattices forming the atomic structure of the graphene. This gives D(φ)=1/3πr02 which is constant with respect to φ. As shown in the previous section, the value of the multi-body coupling term Bij is very close to one for graphene. Further, since the attention of this article has been given the stability characteristics of SLGSs rather than the atomic arrangement of carbon bonds, Bij can be approximated by one. This yields the equilibrium bond length to be found as R(e) from Eq. . Regarding the forgoing approximations, the continuum strain energy density can then be evaluated from the energy stored in atomic bonds by averaging over the bond orientations and distribution asThe second Piola – Kirchhoff stress T is the work conjugate of the Green strain E given byIn the linear regime, the stress is related to the strain via the modulus tensor C aswhere C is obtained from the total derivative of T with respect to E asC(E)=13πR(e)2∫02πV″(r)r2−V′(r)r3nij(0)nij(0)nij(0)nij(0)dφAt infinitesimal strain, the linear elastic modulus of an SLGS can be found from this continuum theory by taking a vanishing Green strain, E = 0 (i.e., no deformation), in Eq. . The only nonzero components of tensor C are Cyyyy = Cxxxx, Cyyxx = Cxxyy = Cxyyx = Cxyxy = Cyxxy. Therefore, Eq. [TxxTyyTxy=Tyx]=[CxxxxCxxyy0CyyxxCyyyy0002Cxyyx][ExxEyyExy=Eyx]Use of the nonlocal theory makes the long range interatomic reactions to be taken into consideration and then the nonlocality to be brought into the continuum modeling. In fact, this theory introduces the small scale effects into the constitutive relations as a material parameter σij(x)=∫λ(|x−x′|,α)Cijklεkl(x′)dV(x′),forxεVwhere σ, ε and C denote the nonlocal stress, strain and forth-order elasticity tensors, respectively. |x−x′| is the Euclidean distance and the kernel function λ(|x−x′|,μ) represents nonlocal modulus incorporating the nonlocal effects at the reference point x into the constitutive relations. V denotes the volume of body and α is a material constant defined as α=e0a/l in which e0, a, and l denote a constant suitable to each material, internal characteristic length (e.g., lattice spacing, granular size, length of C–C bonds) and external characteristic length (e.g., crack length, wavelength), respectively. Eringen proposed a single partial differential form of Eq. which is called as the basis of the nonlocal constitutive formulation aswhere μ = α2l2 = (e0a)2 is the nonlocal parameter, ∇2 the Laplacian operator given by ∇2=∂2∂x2+∂2∂y2 and ‘:’ the double dot product. By setting e0a to zero, the nonlocal continuum theory reduces to its classical or local counterpart.In this article, an elastic rectangular plate of length a in the x direction, width b in the y direction and thickness h in the z direction, shown in , is used for modeling an SLGS. In order to leave the formulation out of Young's modulus, the elasticity tensor in Eq. is replaced by the elastic modulus tensor obtained based on the interatomic potential in Section . This gives the nonlocal constitutive relation aswhere the thickness of the SLGS, h, appears in the right hand sides because the strain energy density has been defined as the energy per unit area making the linear elastic modulus tensor C to be actually the linear elastic tensile stiffness rather than modulus. Based on the classical plate theory, the strain-displacement relationships are given by εxx=−z∂2w∂x2,εyy=−z∂2w∂x2,εxy=−z∂2w∂x∂y,γxz=γyz=0where w is the transverse displacement. By the use of the principle of virtual work, the following equilibrium equation can be expressed for CLPTwhere q indicates the transverse load applied and {Mxx, Myy, Mxy} are the moment resultants which are defined based on the components of the stress in Eq. and can then be expressed as follows by using Eq. Mxx=∫−h2h2σxxzdzi.e.Mxx−(e0a)2∇2Mxx=−112h2(Cxxxx∂2w∂x2+Cxxyy∂2w∂y2)Myy=∫−h2h2σyyzdzi.e.Myy−(e0a)2∇2Myy=−112h2(Cxxxx∂2w∂y2+Cxxyy∂2w∂x2)Mxy=∫−h2h2σxyzdzi.e.Mxy−(e0a)2∇2Mxy=−112h2(Cxyyx+Cxyxy)∂2w∂x∂y, the governing equation of motion for the nonlocal atomistic-based plate model can be obtained in terms of the lateral deflection w as−h212cxxxx(∂4w∂x4+∂4w∂y4)−h26(cxxyy+2cyxxy)∂4w∂x2∂y2=ρh∂2w∂t2−ρh(e0a)2(∂4w∂x2∂t2+∂4w∂y2∂t2)+qIn order to solve the vibrations problem, the deflection functions satisfying the boundary conditions need to be first determined. To this end, we adopt the approach of Radhakrishnan et al. where Wmax is the maximum deflection of the monolayer GS under a uniformly distributed load q and F(x,y) is the mode shape function. Substituting Eq. and then applying the Galerkin method yields∬A(−h212cxxxxWmax(∂4F∂x4+∂4F∂y4)−h26(cxxyy+2cxyyx)Wmax∂4F∂x2∂y2−q)Fdxdy=0The preceding equation can be rewritten in the following simplified formRΓ=∬A(−h212cxxxx(∂4F∂x4+∂4F∂y4)−h26(cxxyy+2cxyyx)∂4F∂x2∂y2)Fdxd,SΓ=∬AFdxdyThe transverse displacement function for free vibration of the monolayer GS is taken to bewhere ω is the angular frequency. Now, using Eq. , the Galerkin algorithm is applied again to Eq. , one can finally get the fundamental frequency relation asThe mode shape functions for different boundary conditions are given by SSSF: Two opposite long edges simply supported, remaining ones simply supported and freeSSCS: Two opposite long edges simply supported, remaining ones clamped and simply supportedFFSS: Two opposite long edges freely supported, remaining ones simply supportedSSCC: Two opposite long edges simply supported, remaining ones clamped and manipulating the resulting equations, the following frequency explicit relations for the single-layer graphene sheets with different edge conditions are obtained.ω=0.0084(−1+cos(πba))(−1+cos(πab))π6h2×((b4+a4)Cxxxx+2a2b2(4Cxyyx+Cxxyy))/a2b2(a2b2+9.869μ(b2+a2))(−1+cos(baπ))×(−1+cos(abπ))ω=−(0.026(−1+cos(πab))π5Cxxxxh2)/b2(b2+9.869μ)×(−1+cos(abπ))ω=−(0.487h2((−249.6b4−974a4)Cxxxx−a2b2(243.5Cxxyy+974Cxyyx)))/a2b2(−5.844a2b2−μ(72.10b2+57.68a2))ω=−(0.0265(−1+cos(πba))π5Cxxxxh2)/a2(a2+9.869μ)(−1+cos(baπ))ω=−(0.974h2((157b4+157a4)Cxxxx+a2b2(104.7Cxxyy+418.8Cxyyx)))/a2b2(3.534a2b2+46.5μ(b2+a2))ω=−(1.948h2((104.7b4+19.63a4)Cxxxx+a2b2(52.3546Cxxyy+209.4Cxyyx)))/a2b2(4.712a2b2+μ(62.01b2+46.50a2))The effective thickness and the mass density of the monolayer graphene sheet for numerical analysis are taken to be ρ = 2250 Kg/m3, h = 0.34 nm, respectively Cxxxx=Cyyyy=2291.50 eV·nm−2,Cxxyy=Cxyyx=763.83 eV·nm−2Before studying the various parameters on vibrational behavior of the graphene, the numerical results are compared with the results of MD simulations to demonstrate the efficiency of the present formulas. The simulations are performed herein by the use of the molecular dynamics simulator “NanoHive” shows the comparison of the natural frequency of the square SLGSs with all edges simply supported for different side lengths. From this figure one can observe that the present results are in good agreement with those of MD simulations. To further verify the effectiveness of the current explicit expressions, the frequency ratios (the nonlocal frequency (μ ≠ 0) to local frequency (μ = 0) ratio) of an all edges clamped square monolayer graphene sheet for three nonlocal parameter (μ = 1, 2, 3 nm2) are evaluated by using Eq. and results of which are compared with those of Ref. . Again, a good agreement between two sets of results is found which confirms the validity of the present formulae. Moreover, from this figure it can be seen that as the side length of the SLGS goes up the frequency ratio goes up, too and approaches one. In other words, the size effects on natural frequency of the SLGSs are lessened at higher side length. In fact, this observation verifies the capability of the local continuum theories in analysis of the large-scale nanostructures. shows plot of the natural frequencies of the square graphene with the nonlocal parameter μ = 2 nm2 against side length for different boundary conditions. As depicted in this figure, the maximum frequency is obtained for the SLGS with CCCC edge conditions and the minimum frequency is obtained for one with SSSF edge supports. Further, it is observed that with the increase of side length the natural frequency and also the difference between the frequencies corresponding to different boundary conditions are decreased. Variation of the frequency ratios of the SLGSs with aspect ratio (a/b) for different boundary conditions at the scale parameter μ = 2 nm2 are indicated in with the assumption of a = 10 nm. It is seen from this figure that, as the aspect ratio increases, the nonlocal effect diminishes and the results from the nonlocal model tend to those of local model. It is also observed that the curve corresponding to the SSSF boundary conditions is over the others. This may be attributed to the fact that the importance of the small length scale is affected by the kind of boundary conditions selected, so that the nonlocal effect is less prominent for softer boundary conditions.In order to see the sensitivity of the SLGSs with various edge supports to scale effects, the frequency ratios of the square monolayer graphene sheets versus nonlocal parameter for different boundary conditions are graphed in . The side length is taken to be 10 nm. As observed, when the nonlocal parameter becomes larger the frequency ratios reduce, that is, the introduction of the small scale effects into the modeling leads to the lower frequencies. Regarding this figure, the type of boundary condition influences the prominence of the small length scale effects in natural frequency such that the all edges clamped SLGS shows the most sensitivity to small scale effects and the SLGS with SSSF edge conditions indicates the least one.In this work, the interatomic potential was incorporated into a nonlocal plate theory to develop a Young's modulus-independent nonlocal model for studying the vibrations of graphene. By applying the Galerkin approach, explicit relations for the fundamental frequency of the monolayer graphene sheet with various edge supports were derived from its static deflection due to a uniformly distributed load. Through comparison of the present results and ones from MD simulations and the other previously reported ones, the present formulae were found to have the capability to reproduce the frequency of the SLGSs in a simple and quick way. It was discerned that the magnitude of the natural frequency and the prominence of the size effects are influenced by the type of boundary conditions such that the harder edge supports, the higher natural frequency and the more sensitivity of the SLGS to small scale effects. However, these differences between the boundary conditions are smaller for the SLGSs with high side length.Fluid inclusion and sulfur and oxygen isotope studies on quartz-carbonate-sulfide veins of the Carvoaria Velha deposit, Córrego do Sítio gold lineament, Quadrilátero Ferrífero, Minas Gerais, BrazilThe Córrego do Sítio lineament is defined as a 16-km long, NE-SW-trending ductile shear zones, which controls fourteen gold deposits, including the Carvoaria Velha deposit. The dominant lithotypes of this deposit are metagrewackes with subordinate carbonaceous phyllites lenses of the Archean Rio das Velhas greenstone belt, which host gold mineralization. Metamafic dikes and sills are parallel and crosscut the host metasedimentary sequence. All these rocks exhibit alteration to quartz, carbonate and sericite, besides sulfides and sulfosalts. The main gold mineralization styles at the Carvoaria Velha deposit, and at Córrego do Sítio as a whole, are quartz-carbonate-sulfide ± sulfosalt veins of varied distribution. The veins are classified as: V1 veins – quartz-ankerite-pyrite-berthierite-gold – parallel to the main regional foliation Sn,; V2 veins – quartz-ankerite-pyrite – developed at extensional crenulation cleavage Sn + 1, and rarely gold mineralized; V3 veins – quartz-ankerite – filling Sn + 3 fractures, usually free of sulfides and sulfosalts; V4 veins – quartz-calcite – of restricted occurrence in metamafic dikes and sills. The latter crosscut the metasedimentary sequence, are extensional and display no preferential orientation. The most common ore minerals in all vein types are arsenopyrite, pyrite, berthierite, and pyrrhotite. Microprobe analyses reveal the presence of metallic phases rich in Sb, Pb and Co, such as stibnite, ullmanite, tetrahedrite, galena, cobaltite, which commonly overgrow the sulfides. Fluid inclusion studies trapped in quartz from V1, V2 and V4 veins have identified a H2O-CO2 |
± CH4-NaCl mineralizing fluid that may contain KCl, MgCl2 e FeCl2. The presence of CH4 in fluid inclusions of the V1 and V2 veins reflect interaction of the fluid with the Córrego do Sítio and Santa Quitéria carbon-bearing metapelitic host units.Based on the microthermometric data, the hydrothermal fluid is interpreted to have evolved in at least two stages: i) an early fluid stage, trapped in smoky quartz, of moderate salinity (~ 8.5 eq. wt% NaCl), and minimal trapping temperature of 330 ± 17 °C; and ii) a late-stage fluid trapped in recrystallized quartz with lower salinity (~ 4.6 eq. wt% NaCl), and a minimal trapping temperature of 365 ± 33 °C. Isotopic values of δ18Ofluid (+ 7.9 and + 13.0‰), Δ33S (+ 0.3 to + 3.5‰) and δ34S (− 2.9 to + 6.1‰) suggest that indeed the hydrothermal fluid responsible for the gold mineralization at the Carvoaria Velha deposit must have had a metamorphic origin, and interacted with metasedimentary sequences during its ascending path. The addition of CH4 during fluid-rock interaction may have caused some decrease in ƒO2 of the fluid which, as a consequence, destabilized gold-bearing sulfur complexes, liberating S− 2 for the formation of Fe sulfides and sulfosalts (arsenopyrite, pyrite, pyrrothite and berthierite, etc.), and outcome gold deposition.The Quadrilátero Ferrífero (QF) region represents an important Brazilian metallogenetic province located at the southern border of the São Francisco Craton. This province is one of the world’s largest producers of mineral resources, such as gold and iron ores, with a number of world-class gold deposits hosted by Archean rocks of the Rio das Velhas greenstone belt (Other than gold deposits, such as Pilar () and the historically banded-iron-formation-hosted (BIF) gold producer São Bento mine (), the region near Santa Bárbara is also known for large iron ore mines, including Brucutu and Gôngo-Soco (The 16-km long, NE-SW-trending Córrego do Sítio regional gold lineament () is located in the northeastern part of the QF, at the Brumal district, town of Santa Bárbara, where fourteen gold excavations and two geochemical anomalies are found (). The term Córrego do Sítio lineament was proposed by to include several gold occurrences along a NE-SW trend with similar lithostratigraphic characteristics.In 1981, while seeking the continuity of the São Bento ore bodies, the Córrego do Sítio gold lineament was discovered, through geological mapping and soil geochemical analysis (). At the Córrego do Sítio lineament, the Nova Lima Group, Rio das Velhas greenstone belt, comprises a succession of metamorphosed, carbonaceous turbiditic, graywacke-siltstone-shale and slates that hosts lode-gold mineralization associated with quartz-carbonate-sulfide veins (). The Cachorro Bravo, Laranjeiras, and Carvoaria Velha are the main ore deposits, and they are all characterized by the same lithological sequence. Its open-mine exploitation took place between 1990 and 1998, and restarted in 2002 with an accumulated production nearing 11 tons of gold (), by AngloGold Ashanti Brasil Mineração (AGABM). The probable and proven ore reserves at Córrego do Sítio deposits currently stand at 411,000 oz of Au with an average grade of 6.42 Au g/t (sulfide and oxide ores; The present study focuses on the Carvoaria Velha deposit (B) encompassing petrographic, alongside mineral chemistry studies in carbonates and sulfides, and fluid inclusions and O18 and S34 isotopic studies in order to understand and characterize the hydrothermal fluid involved in the gold mineralization. These are intended to contribute to the geological knowledge of the Nova Lima Group gold deposits of the QF region, as few previous isotope and fluid inclusion work exist (), none of which for the Córrego do Sítio lineament.In order to do so, this article presents the following specific aims: (i) Classify different vein types in the Carvoaria Velha orebody and host rocks; (ii) Analyze the composition of the hydrothermal fluids in quartz crystals; (iii) Define the physical-chemical conditions (P-T-composition) and probable sources of fluids (metamorphic/magmatic/meteoric water) associated with the hydrothermal and structural events.The procedures for sampling and the methods of analyses were the following:Sampling of quartz-carbonate veins mainly from drill core FCS 926 (), as well as galleries of the Laranjeiras (level 696) and Cachorro Bravo (level 643) deposits, with selection of samples was done in such a way to represent all vein types, ranging from mineralized to non-mineralized portions;Macro- and microscopic petrographic studies focused on quartz-carbonate veins and veinlets, with definition of petrographic characteristics;Electron microprobe analyses were performed on carbonate and sulfide crystals using the JEOL model JXA 8900RL, at the Electronic Microscopy and Microanalytical (LMA) Laboratory at the Physics, Geology and Chemistry-CDTN-CNEN Consortium Laboratory, at the Universidade Federal de Minas Gerais, UFMG, Brazil. The following analytical conditions were used: accelerating voltage 15 kv, beam current 20 nA, count time 10 to 100 seconds, detection limits (ppm) varying for each analysed spot, lowest for Ca (144), Mg (110), Fe (421), Mn (452), S (100), Fe (250), Co (220), Ni (250), Cu (250), As (200), Sb (280), Pb (800), Au (310), Zn (280) and Ag (170), standards Ian Steele, Smithsonian Institute and Astimex, ZAF correction program;Detailed petrographic mapping of fluid inclusions (FIs) in gold mineralized vein and breccia quartz and carbonate crystals was undertaken to discriminate inclusion types, sizes, morphologies and definition of fluid inclusion assemblages (FIA). A Leica petrographic microscope was used, with 10 × oculars and objective lenses of 2.5 ×, 5 ×, 10 ×, 20 ×, 50 × and 63 ×;Fluid inclusion microthermometric studies were conducted using a fully automated Linkam THMSG600 heating and freezing stage with a TMS 93 temperature controller. The stage was calibrated between – 56.6 °C and 374.1 °C with synthetic fluid inclusion Linkam standards (pure H2O and mixed H2O-CO2). The cyclic technique () was used to acquire better precision in measurements of transition of temperature between carbonic phases. The accuracy of the freezing measurement runs is about ± 0.1 °C and for heating runs ± 1 °C between 200 and 500 °C. Apparent salinity has been reported in equivalent percentage weight of NaCl. Calculations of salinity and density were made using the MacFlinCor program (Raman spectroscopy was used to assess gases and fluids contained within the FIs. This technique allows a correlation between the composition and phase behavior, during the studies of cooling of FIs. Raman spectra were obtained on a Jobin Yvon/Horiba LABRAM-HR 800 spectrographer equipped with a He-Ne laser (632.8 nm). The Raman signal was collected by a BX-41 Olympus microscope using 10 ×, 50 × and 100 × objectives. The acquisition time ranges from 10 to 120 s, depending on sample background fluorescence, and the laser power from 0.06 to 6 mW. Spectra were acquired 10-30 times to reduce signal/noise ratio. Collected Raman spectra were analyzed and optimized with Labspec 4.18 and Origin 8.0. Background was corrected and when necessary normalized and peak deconvoluted. Measurements were performed at the Raman Laboratory of Spectroscopy in the Department of Metallurgic and Materials Engineering at UFMG;In situ O isotopes in quartz and S isotope in chalcopyrite, pyrite, and pyrrhotite measurements were measured using a Cameca IMS 1280 multi-collector ion microprobe located at the Centre for Microscopy, Characterisation and Analysis (CMCA), University of Western Australia. The samples consisting of rock fragments were cut from slabs and mounted with the standard UWQ-1 (12.33 ± 0.01‰ VSMOW; ) in 25.4 mm epoxy discs for oxygen isotopes or in-house standards SON-1 δ33S = 0.78 ± 0.06‰ VCDT, 1 SE, n = 3 and δ34S = 1.45 ± 0.08 VCDT, 1 SE n = 3) for S isotopes. Oxygen isotope ratios (18O/16O) were determined using a static ~ 3 nA Cs + beam with an impact energy of 20 keV focused to a 10-15 μm spot on the sample surface. Instrument parameters included: a magnification of × 133 between the sample and field aperture, 400 μm contrast aperture, 4000 μm field aperture, 110 μm entrance slit, 500 μm exit slits, and a 40 eV band bass for the energy slit with a 5 eV offset to the high-energy side. Secondary O- ions were accelerated to 10 keV and analyzed with a mass resolving power of approximately 2200 (10% max peak height) using dual Faraday cup detectors. A normal incidence electron gun was used for charge compensation. Each analysis spot was pre-sputtered for 10 seconds before automated peak centering in the field and contrast apertures was performed. Analyses consisted of twenty-four second cycles, which gave an average internal precision ~ 0.1‰ (1 SE). Bracketing standards allowed correction for instrumental mass fractionation (IMF) which was corrected using standard UWQ-1. The average spot-to-spot reproducibility (external precision) of the standard was less than 0.15‰ (1SD). On some mounts NBS-28 was analysed as an unknown and returned an average value of 9.4 ± 0.3 which is in good agreement to the recommended value (9.6 ± 0.1‰, 1 SD). Sulfur isotope ratios 33S/32S and 34S/32S were determined using triple Faraday cup detectors and similar conditions to above with the following exceptions. The analyses used a ~ 1.5 nA focused Cs+ beam and 80 μm entrance slit and the sample was presputtered a 20 μm × 20 μm for 30 s Following the presputter phase, the raster was reduced to 10 μm × 10 μm with dynamic transfer employed to center field and contrast apertures prior to acquiring 16 × 4 s cycles. The 33S detector was offset to the low mass side to avoid interference from 32SH-. Internal precision for S-isotope analyses averaged 0.06‰ for δ33S, and 0.03‰ for δ34S. External precision averaged 0.08‰ for δ33S, 0.07‰ for δ34S, and 0.08‰ for Δ33S. We define Δ33S as Δ33S = δ33S–1000×[(1 + δ34S/1000)0.515 − 1]. Data was reduced and uncertainties propagated following . Uncertainty terms included internal precision, the uncertainty of the values of the working standards relative to VSMOW or VCDT and the external precision of the standards measurements defined by a weighted average of the individual instrumental mass fractionation factors.The QF region is located in the southern part of the São Francisco Craton (). The QF includes: 1) granite-gneiss complexes, corresponding to the crystalline basement; 2) Archean greenstone belt tracts belonging to the Rio das Velhas Supergroup; and 3) Proterozoic metasedimentary units, represented by the Minas Supergroup, the Itacolomi Group and the Espinhaço Supergroup (Granite-gneissic complexes have trondhjemite-tonalitic-granodioritic (TTG) composition, and correspond to polideformed gneissic rocks and subordinately by granites, amphibolites and mafic and ultramafic intrusions (). They are represented by the Bonfim, Caeté, Belo Horizonte, Bação, and Santa Bárbara complexes (). The TTG complexes are intruded by granitoids of variable compositions, comprising foliated, poorly and nonfoliated types, and ranging from apophyses to large bodies (). Geochronological data reveal these complexes formed in between 3380 Ma to 2900 Ma (), with migmatization between 2860 ± 14 Ma and 2772 ± 6 Ma. They were affected by the Transamazonian Orogeny and record metamorphism at 2041 ± 5 Ma (The Archean Rio das Velhas greenstone belt corresponds to a metavolcanosedimentary sequence divided, from base to top, into the Nova Lima and Maquiné groups, respectively (). The Nova Lima Group is composed of a basal unit formed by tholeiitic-komatiitic volcanic rocks, associated with chemical sedimentary rocks; a volcaniclastic intermediate unit, associated with felsic volcanism; and an upper unit with clastic sedimentary rocks ( described komatiites at the base of the sequence, naming them as the Quebra Ossos Group. The largest gold deposits in the Quadrilátero Ferrífero are hosted in the basal sequences of greenstone belt Rio das Velhas (The Maquiné Group is divided in the basal Palmital Formation (), consisting of quartzite and quartz phyllite, and the upper Casa Forte Formation () composed of sandstones and conglomerates. propose a stratigraphic subdivision of the Rio das Velhas greenstone belt, Nova Lima Group, on the basis of lithofacies associations encompassing, from the basal part to the top, the mafic-ultramafic volcanic, volcano-chemical-sedimentary, clastic-chemical sedimentary, volcaniclastic, resedimented, coastal and non-marine associations. (i) The mafic-ultramafic association is predominantly composed of basalts as massive and pillow flows, with minor gabbro, anorthosite and peridotite, and intercalations of banded iron formation, ferruginous chert, carbonaceous pelite, turbidites, and rare felsic volcanoclastic rocks. (ii) The volcano-chemical-sedimentary association has tholeiites intercalated with BIF and ferruginous chert, and subordinated fine-grained clastic sedimentary rocks, turbidites and pelites, which are intercalated with chemical rocks. (iii) The clastic-chemical sedimentary association is composed of alternating fine-grained pelites (micaceous and chloritic schists) with lesser BIF, and subordinate chert and carbonaceous schists. It corresponds to the Santa Quitéria unit in the study area. (iv) The volcaniclastic association is composed of volcaniclastic felsic and mafic rocks. (v) The resedimented association is widely distributed in the QF and comprises mainly graywackes, quartz graywackes, sandstones, and siltstones. It corresponds, on its east and north sectors, to the Mindá and Córrego do Sítio units, both present in the study area. (vi) and (vii) The coastal and non-marine associations correspond to sandstone-siltstones and sandstones-conglomerates, respectively.The U-Pb ages of detrital zircon from volcanoclastic rocks of the Nova Lima Group have confirmed felsic volcanism with an age of 2772 ± 6 Ma (), and a minimum depositional age of 3.029 Ga (The Proterozoic metasedimentary units include the Minas Supergroup, Itacolomi Group, and Espinhaço Supergroup. The Minas Supergroup () is a metasedimentary sequence interpreted by as formed in an intracratonic basin. On the other hand, interpret it as a supracrustal platform sequence developed in a sialic substrate. This supergroup is laid unconformably over the Archean Rio das Velhas greenstone belt (GBRV), and it is composed of metamorphosed chemical/clastic sediments with quartzite, metaconglomerates, metapelitic rocks and a thick sequence of Lake Superior Type banded iron formation (BIF) that hosts high-grade (~ 64% Fe) iron orebodies (). The Itacolomi Group is represented by immature clastic sediments () and contains zircon with a minimum age of 2060 Ma (LA-ICPMS Pb-Pb in zircon; ). The Espinhaço Supergroup covers a small area in the QF, set over the Minas Supergroup along an angular unconformity, and represents a rift sequence that includes breccias, conglomerates and quartzite. Its development is related to a Siderian-age rifting (), which led to both continental and marine deposition of clastic sediments between 1840 and 1714 Ma (U-Pb; The QF has a geometry delineated by synform and antiform mega folds that, in its eastern portion, are truncated by north-south thrust faults (). The QF is limited at north, south, west and east by the regional synclines of the Serra do Curral, Moeda, Dom Bosco, and Santa Rita (and probably the Gandarela syncline; describe in the QF a dome-and-keel structure, in which the basement occurs as domes (e.g. Bação, Bonfim, Santa Bárbara, etc.) that are circled by keels containing rocks of the Archean Rio das Velhas greenstone belt and the Minas Supergroup. They also state that shear zones exist along the contacts between supracrustal and basement rocks in all domes.There are various interpretations and tectonic-structural evolution models proposed for the QF. However, different authors (see ) share the opinion that there was more than one deformation and metamorphism event in order to the regional structures of the QF to be obtained. presents a summary of significant studies on the tectonic-structural evolution of the QF.The Córrego do Sítio lineament is located in the northeastern sector of the QF region (A). The term Córrego do Sítio lineament was proposed by to include several gold deposits and occurrences along a NE-SW trend, where Carvoaria Velha is located. Together with Cachorro Bravo, Laranjeiras (A), Bocaina, and Crista, they all show similar lithostratigraphic characteristics. According to , the lithostratigraphic units of this sector are grouped in the clastic-chemical and resedimented lithofacies associations of the Rio das Velhas greenstone belt, formerly referred to Santa Quitéria and Córrego do Sítio units of , respectively. These are associated with the upper Nova Lima Group, dipping to the east over rocks of the Mafic-ultramafic association (previously named as Quebra Ossos Group by The Córrego do Sítio lineament is dominated by rocks of the resedimented and clastic-chemical sedimentary lithofacies association, Córrego do Sítio and Santa Quitéria units, respectively. In the study area, these units correspond to an alternation of metapelites and metapsamites, with gradational layering and plane-parallel and cross-bedding stratification. Subordinate thin levels of carbonaceous phyllites and BIF are present. These units are interpreted by as a result of deposition by turbidity currents. They are classified as quartz-carbonate-white mica-chlorite schists, and represent the product of the greenschist facies metamorphism of graywackes, sandstones and pelites, according to ). There is still a swarm of metamafic dikes and sills of uncertain age, in general subparallel to the metasedimentary sequence; they possess various orientations, mainly NE-SW, and dip to the SE, (). These constitute tabular bodies of metric and decametric thickness, and kilometric continuity, composed of metagabbros in different zones of hydrothermal alteration to carbonate, chlorite and sericite (). There are four types of dikes, locally named as DB1, DB2, DB3, and DB4. Whereas DB1 exhibits moderate hydrothermal alteration with chlorite and carbonate formation, DB2 and DB3 are very altered to carbonate and muscovite. DB4 is incipiently altered to chlorite and still preserves relicts of pyroxene. The Córrego do Sítio lineament is loci to various gold deposits, the most important being the Cachorro Bravo, Laranjeiras and the Carvoaria Velha, shown in A. These deposits all have analogous characteristics (e.g., The region is structurally controlled by the Gandarela Syncline and Conceição Anticline of the Minas Supergroup, and they are truncated by the Fundão and Água Quente fault systems (Orogenic gold mineralization in the Córrego do Sítio lineament is structurally controlled and associated with hydrothermal alteration that gave place to the development of chlorite, carbonate, sericite, sulfide-sulfosalt, and massive amounts of silica. Because of the nature of the metasedimentary rocks, the contrast between pre-altered and altered sequences is very subtle, and has been dealt with in detail by shows a summary of the paragenetic sequence related to the hydrothermal alteration halos, from distal to proximal in relation to gold mineralization.Two main gold mineralization styles are recognized at the Córrego do Sítio lineament: 1) disseminated sulfide-associated ore in metasedimentary rock, parallel to the main foliation; 2) in quartz-carbonate-sulfide ± sulfosalts veins of varied distribution, with the dominance of free gold in quartz. In the disseminated ore, gold is present as inclusions in fine-grained sulfides (< 100 μm), essentially arsenopyrite, pyrrhotite and pyrite, developed in different alteration stages (), some of them during the deformation (). Sulfides form anastomosing micro lenses along layers of carbonaceous quartz-sericite phyllites or schists, or metagraywackes of the Córrego do Sítio unit (). In quartz-carbonate-sulfide ± sulfosalts veins, gold is present as i) inclusions in sulfides, such as pyrite and pyrrhotite, ii) inclusions in sulfosalts, and iii) free crystals in quartz together with sulfides. Sulfosalts include berthierite, tetraedrite-tennantite, ullmannite, and gersdorfite. Veins may form a dense network, considering that in mineralized lodes they are narrow and long, lenticular, boudinaged, and locally ruptured.Based on mineralogical composition and mineral textures, identified gold in five associations: 1) free and disseminated electrum in quartz-carbonate veins; 2) included in disseminated arsenopyrite, generally parallel to the main foliation (Sn), and associated with phyllosilicates-rich (chlorite, sericite or muscovite) portions; 3) included in berthierite; 4) included in pyrite or pyrrhotite that are disseminated parallel to the main foliation in micaceous portions; 5) included in silicates, such as quartz or muscovite.For the present study, the mineralized samples contain ore grades of up to 26 g/tons Au (), and correspond to ore of the second mineralization style, that is, quartz-carbonate-sulfide ± sulfosalt vein, with ore minerals represented by arsenopyrite, berthierite, pyrite and pyrrhotite.The mineralized rocks at the Córrego do Sítio lineament are associated with NE-SW, dextral ductile shear zones. The lineament is actually a composite structure, with two main mineralized branches, which strike subparallel to each other, separated by approximately 350 m true thickness of phyllites (). The structures at the Córrego do Sítio lineament resulted from a complex evolutionary tectonic history developed in at least three deformational events (). The statistical structural analysis applied to the Bocaina, Cachorro Bravo, Carvoaria Velha, Crista, and Laranjeiras deposits ( to define the main phases of deformation presented in The first event (Dn) followed the deposition of the sedimentary rocks and produced tight, asymmetric and disharmonic, kink folds, which gave place to an axial planar foliation (Sn) striking NNE, and moderately to steeply-dipping to ESE (). Although Sn is the main regional foliation, because it dips subparallel to bedding, it is difficult to distinguish them from one another. There are rock strips that show mylonitic foliation (Sn mylonitic) subparallel to Sn, which are interpreted to be contemporaneous and cogenetic to Sn, reflecting a strong shearing component of a single progressive event.The second event (Dn + 1) is represented by a crenulation cleavage (Sn + 1) striking NNE, crosscutting Sn at a high angle (70−80°) to the northwest. interprets Dn + 1 as an extensional crenulation cleavage, possibly representing a late phase of Dn. The third event (Dn + 2) created open folds that arched the bedding, the foliation Sn and the crenulation cleavage Sn + 1, maintaining the high angle between Sn and Sn + 1 without the development of a pervasive foliation. The Dn + 2 event is better recognized near the surface than in deeper levels. The fourth event (Dn + 3) is associated with the formation of structures in transitional ductile-brittle conditions. Parallel fractures predominate, spaced from centimeters to meters along with open folds or subordinate kink folds. The open folds have steeply-dipping axial plane and strike mainly towards NW.In all lithotypes of the Carvoaria Velha deposit (), millimetric to metric veins are composed mainly of quartz and carbonate, and may contain sulfides and sulfosalts. The presence of these minerals is not directly related to economic gold grade. For a better understanding of mineralization and the complex distribution of veins, different vein types have been classified for the purpose of the fluid inclusion studies, and also for the understanding of the structural evolution and hydrothermal alteration (). Mineralized veins are only hosted in the metasedimentary rocks. Samples were selected mainly from the 926 drill core (), Carvoaria Velha deposit, as well as galleries of the Laranjeiras (level 696) and Cachorro Bravo (level 643) deposits., studied veins are classified based on their structure and mineralogy in types V1, V2 and V3, hosted in metasedimentary rocks, and V4, hosted in metamafic dikes and sills.V1 vein type – Quartz-ankerite-pyrite-berthierite-gold (< 6 m thickness) – these veins have varied geometry and correspond to irregular lenses that may be folded, boudinaged, and locally exhibit pinch-and-swell structures (). They are usually discontinuous, parallel to the main regional foliation Sn, sheared, and may be mineralized in gold.V2 vein type – Quartz-ankerite-pyrite (< 3 m thickness) – these veins develop along the extensional crenulation cleavage (Sn + 1), and are not mineralized.V3 vein type – Quartz-ankerite (< 20 cm thickness) – these veins form continuous lenses, filling Sn + 3 fractures, and are locally brecciated and present saccharoidal texture. Sulfides are very rare.V4 vein type – Quartz-calcite (< 15 cm thickness) – veins of restricted occurrence in metamafic dikes (DB1 dikes), with brecciated and lenticular geometry, showing no preferable orientation.Microscopically, quartz (65–80% of total volume) and carbonates (5–20% of total volume) are the most abundant minerals in the veins. They form fine to medium-grained (0.2–4.0 mm) euhedral and anhedral crystals, with polygonal and irregular contacts. There are two groups of quartz crystals: (i) medium-grained (up to 4.0 mm), smoky quartz (QtzI), showing evidence of deformation such as subgrain formation and undulose extinction; and (ii) granoblastic, fine-grained quartz (QtzII), with straight extinction, rarely undulose, which is product of QtzI recrystallization (). Carbonates also form two groups: stained and twinned, medium-grained crystals (Carb I) and clear, finer-grained aggregates classified as Carb II (Sulfides and sulfosalts are disseminated in all vein types, forming aggregates with fine to medium-grain size. Where abundant, they constitute up to 8% of the vein total volume. The most abundant sulfides and sulfosalts are pyrite, chalcopyrite, arsenopyrite, pyrrhotite, and berthierite. Stibnite, galena, boulangerite, ullmannite, tetraedrite, argentopentlandite and cobaltite are rare and restricted to V1, where they may overgrow the most abundant sulfides and sulfosalts, and are only identified via microprobe analyses.Among the opaque minerals in vein types V1, V2 and V3, pyrite (Py) is the most common, forming fine to medium-grained (< 4.0 mm) disseminated crystals. It is porous and anhedral Py(I) and polygonal subhedral Py (II).Arsenopyrite (Apy) is present along the border of V1 veins or in thin rock chips within these veins, subparallel to the main foliation, commonly disseminated in micaceous bands of metapelites. Fine-grained crystals (0.4 mm) are represented as: anhedral masses of Apy(I) associated with pyrrhotite; euhedral fine-grained Apy (II) crystals, with clear surfaces and diamond-shape, overgrowing pyrite or pyrrhotite crystals (Berthierite (Bert) is restricted to type 1 V1 veins, and dispersed throughout the veins, in fine to coarse-grained anhedral crystals (< 8.0 mm). Locally, it seems to overgrow carbonate and pyrite (E). It may contain pyrite, pyrrhotite and chalcopyrite inclusions (C). Chalcopyrite (Cpy) (< 0.4 mm) forms aggregates throughout these veins. It is overgrown by other phases such as cobaltite (G), pyrrhotite and argentopentlandite. Pyrrhotite (Po) is rare, fine to medium-grained (< 0.1 mm), long and anhedral, oriented according to the main foliation. It also occurs as irregular inclusions in pyrite crystals, or along chalcopyrite edges, where ullmannite and tetraedrite are overgrown (Porous pyrite I, pyrrhotite and arsenopyrite I are chemically zoned, surrounded and corroded by other metallic minerals, suggesting at least two growth phases. Pyrite I and pyrrhotite developed during Dn (), are recrystallized and may be replaced by a second pyrite generation (pyrite II) and by arsenopyrite I. Sulfosalts and gold form in close association with arsenopyrite I.Electron microprobe analyses of carbonates and the main sulfosalt and sulfide minerals were undertaken not only in order to obtain their chemical composition, but also to calculate the arsenopyrite geothermometer according to the criteria of . The following phases were identified and analyzed: arsenopyrite (FeAsS), berthierite (FeSb2S4), ullmannite (NiSbS), tetrahedrite ((Cu,Fe)12Sb4S13), stibnite (Sb2S3), cobaltite (CoAsS), pyrite (FeS2), pyrrhotite (FeS), chalcopyrite (CuFeS2), argentopentlandite (Ag(Fe,Ni)8S8), ankerite (Ca(Fe,Mg,Mn)(CO3)2) and calcite (CaCO3). Their compositions are presented in In pyrite and pyrrhotite crystals, the main detected impurities are Ni (< 0.35% weight) and Zn (< 0.10% weight). The spectrum in shows the standard composition of chalcopyrite crystal, with Fe and Cu depleted edges, which results in an increase of Ni and Co (B and C). Arsenopyrite crystals may be zoned, locally with lighter As-rich nuclei, and also showing a darker nuclei that is depleted in As (). Antimony sulfosalts (ullmannite and tetrahedrite), in addition to cobaltite, stibinite and galena, usually form from pyrrhotite and chalcopyrite alteration (C, G and H). Contents of elements in arsenopyrite are shown in Carbonate crystals were identified in all vein types, and their compositions in V1, V2 and V3 veins are similar, characterized as ankerite, with variations in the oxide concentrations of Mn, Fe and Mg (). Analysis performed on the two carbonate groups (CarbI and CarbII) show similar compositions, presenting differences only on the crystal surface, which are slightly more porous and stained (CarbI), whereas CarbII is clearer (). In V4 veins, hosted in DB1 metamafic dikes, carbonate is calcite ( proposed a “Temperature x atomic concentration of arsenic” diagram as a geothermometer to obtain the temperature of formation for arsenopyrite, considering the following premises: a) arsenopyrirte must be in equilibrium with other sulfide associations (e.g. Py + Apy); and b) concentration of elements such as Co, Sb and Ni, in arsenopyrite, must be lower than 1 wt%.The atomic percentages (% at.) of arsenic in arsenopyrite crystals (Apy I) () from mineralized portions, in equilibrium with gold particles (B), range from 29.2 to 31.3% at. of As (C), these values indicate a temperature of arsenopyrite formation varying from 300 to 375 °C, using the Apy + Py + Po line (A total of nine double polished sections from samples representing the different V1, V2 and V4 vein types that characterize the Carvoaria Velha gold deposit, where fluid inclusions (FIs) are associated with the hydrothermal system were studied for microthermometry and Raman spectroscopy. Fluid inclusions are trapped in the two groups of quartz crystals, namely, QtzI and QtzII (A), the former being smoky as a result of a high number of fluid inclusions (), and contribution of carbonaceous matter; whereas QtzII are recrystallized and almost fluid inclusion free (Petrographic studies show that most inclusions are two-phase, aqueous, liquid-rich with a constant proportion of liquid to vapor (L/V) ratio of 9:1. They have polygonal shapes (rectangular, square and hexagonal), appearing locally as rounded shapes (oval, long and irregular). The average size of inclusions is from 5 to 12 μm in the longest dimension; however, some inclusions may reach up to 30 μm.Fluid inclusions are genetically classified according to their origin in relation to crystal boundaries, and the incidence of both pseudosecondary and secondary fluid inclusions is recorded (A and B). Pseudosecondary inclusions are displayed isolated or in clusters, in random distribution in a single crystal and, locally, in discontinuous trails, without crossing crystal boundaries. These are classified as pseudosecondary, since they do not follow the crystal growth zones. Secondary fluid inclusions are presented in continuous trails that crosscut crystals. They are two-phase aqueous inclusions, show a variable L/V ratio between 9:1 and 8:2, and have oval and irregular shapes. Locally, they are larger than pseudosecondary inclusions, with sizes up to 40 μm.Two main types of fluid inclusions (FIs) are identified based on distribution, shape, size, chemistry, and phases present at room temperature, as well as on microthermometric and Raman spectroscopy data: (i) type 1 – pseudosecondary and secondary aqueous-carbonic H2O-CO2 |
± CH4-NaCl inclusions; and (ii) type 2 – pseudosecondary aqueous H2O + NaCl inclusions. The definition of different salinity systems is based on temperatures of corresponding eutectic points, according to . Type 1 FIs are present in barren or mineralized quartz veins, hosted in metasedimentary rocks. Type 2 FIs are restricted to veins hosted in DB1 metamafic dikes.A Fluid Inclusion Assemblage (FIA) is defined as the most finely discriminated fluid trapping event that can be identified based on petrography (). This definition implies that all inclusions trapped in a specific assemblage represent a fluid of the same composition trapped “at the same time” and, by extension, at the same temperature and pressure (). Based on this statement, four FIAs are identified, type 1 (aqueous-carbonic) with three subdivisions, 1a, 1b and 1c (Pseudosecondary two-phase aqueous-carbonic inclusions are dominant as random clusters, and subordinately in discontinuous trails; secondary inclusions are subordinate. Both are trapped in quartz crystals from V1 and V2 vein types. Raman spectroscopy revealed that the carbonic phase in type 1 inclusions is composed of CO2 and CH4 containing traces of N2 (Pseudosecondary inclusions are restricted to the smoky quartz QtzI (C). They are prismatic in shape (square, rectangular and hexagonal), and locally rounded and oval, ranging in size from 5 to 20 μm, with constant liquid/gas ratio of approximately 9:1. Although three-phase inclusions containing minute, irregular and anisotropic crystals were detected, no dissolution of such crystals could be observed, and therefore these were not considered as daughter minerals.Mainly pseudosecondary inclusions that are restricted to recrystallized quartz QtzII (D). They correspond to rounded and irregular-shaped inclusions, varying in size from 5 to 30 μm, two-phase inclusions at room temperature with liquid/gas ratio of 9:1. They are less abundant than FIA 1a.They are two-phase inclusions at room temperature, forming continuous trails throughout crystal edges, being therefore secondary (B–E). They are oval and irregular in shape, with sizes varying from 4 to 40 μm, and less variable liquid/gas ratios between 7:3 and 9:1. It is possible to observe necking down due to typical deformation of recrystallized quartz.Pseudosecondary two-phase aqueous inclusions present at room temperature, with proportion of liquid/vapor volume of 9:1, and limited to DB1 metamafic dikes. They occur in clusters nearing the centre of quartz crystals, with sizes up to 20 μm (F). Raman spectroscopy revealed that the vapor phase is composed only of H2O. displays microthermometry data, including temperature measurements of the initial ice melting (Te), initial melting of the CO2 phase (TmCO2 ), final melting of ice (Tmice), final melting of clathrate (TmC), homogenization within CO2 phase (ThCO2 L–V), and total homogenization or decrepitation of the inclusion contents (ThTOT). The main phase transitions obtained for FIAs 1 and 2 inclusions during the microthermometry procedure and the information provided by them are summarized in FIA 1 inclusions show low temperatures of the initial melting (Te) between − 48.0 to − 36.0 °C (), with an average of − 43.0 °C, indicating the presence of other cation complexes, such as Fe2 +, Mg2 + and Ca2 +, in addition to Na+ (Borisenko, 1977 in ). Clathrate melting temperatures range from 2 to 9 °C, with an average of 4.6 °C for FIA 1a and an average of 6.6 °C for FIA 1b, and average of 6.0 °C for FIA 1c. Values for CO2 melting temperature range from − 65.3 °C to − 57.0 °C, suggesting the presence of other volatile species besides CO2, as also indicated by the Raman microscopy. Fluid inclusion assemblage 2 inclusions have an initial melting temperature (Te) from − 55.0 to − 45.0 °C (), indicating the presence of other cation complexes additional to Na+, such as Fe2 +, Mg2 + and Ca2 +. The final ice melting temperatures (Tm ice) are lower to those of FIA 1, ranging from − 17.0 to − 7.8 °C.All type 1 inclusions show a size increase in the carbonic phase at temperatures over 250 °C, indicating homogenization into vapor. However, their majority decrepitates before total homogenization, with decrepitation temperatures (Td) between 220 and 340 °C, and averages of Td = 283 °C, 315 °C and 285 °C for FIAs 1a, 1b and 1c, respectively (). Only a few FIA 1b (n = 6) present total homogenization temperatures to vapor (Thtot L-V), with a range of 420 to 460 °C. FIA 2 shows inclusions with homogenization into the liquid (L + V ➔ L) with temperatures between 174 to 215 °C (Salinity, composition and density estimates of aqueous and carbonic phases were calculated using the MacFlinCor software ( were applied to FIAs 1 (H2O-CO2 |
± CH4-NaCl), and equations by for FIA 2 (H2O-NaCl-KCl). A summary of data is presented in . The relative proportions of CH4 and CO2 were estimated using the graphic method by Fluid inclusion assemblage 1 presents variable salinity values, with average of 8.2 eq. wt% NaCl for FIA 1a, 3.7 eq. wt% NaCl for FIA 1b, and 4.6 eq. wt% NaCl for FIA 1c (A-C). Fluid inclusion assemblage 2 is the most saline, with average values of 14.9 eq. wt% NaCl (). Fluid inclusion assemblage 1 is H2O rich, containing between 89 to 98 mol% of H2O (). The FIAs 1a, 1b and 1c show variable proportions of carbonic phase, considering that CO2 is the predominant phase, having similar average values (3.1 mol%) for the three FIAs, reaching maximum values of 6.0, 7.4 and 6.1 mol%, respectively. Concentrations of CH4 are more variable, with FIA 1b (< 3.2 mol%) and 1c (< 2.3 mol%) showing relative higher enrichment to methane when compared to CO2 than FIA 1a (< 1.8 mol%).Total density ranges from 0.95 to 1.07 g/cm3, and 0.96 to 1.01 g/cm3 for FIAs 1 and 2, respectively. The FIA 1a inclusions are slightly denser, average of 1.04 g/cm3, than FIAs 1b and 1c (1.01 g/cm3; Samples for oxygen stable isotopes analyses were selected from the V1, V2, V3 and V4 vein types. A total of 105 in-situ measurements were performed in QtzI and QtzII crystals, in order to identify possible isotopic variations among them. Values of δ18O measured from V1, V2, and V3 veins hosted in metasedimentary rocks vary from + 18.0 to + 14.5‰, and V4 veins (n = 14) hosted in DB1 metamafic dikes vary from + 15.9 to + 14.5‰ (). The temperature of equilibrium for the calculation of fluid isotopic composition (δ18Ofluid) was estimated using homogenization and/or decrepitation temperatures (Th TOT and Td, respectively). The calculated δ18Ofluid values, using the equation of isotopic fractionation by , are similar for V1, V2 and V3 vein types. They comprise an interval of + 7.9 and + 13.0‰ (at 280 to 325 °C), with an average value of + 9.7, + 8.9 and + 9.4‰, respectively (). In the case of V4 vein type, values are lower, from + 2.6 to + 4.1‰, with an average of + 3.2‰ (In-situ analyses of sulfur isotopic composition (δ34S) were performed in eight samples representative of V1 and V4 veins, and on sulfides along the contact of V2 and V3 veins. A total of 71 measurements were made on arsenopyrite, pyrite, berthierite, chalcopyrite, and pyrrhotite crystals (). Sulfides and sulfosalts in V1 mineralized veins show a range of values of δ34S = + 3.1 to 4.8‰ for pyrite, and + 0.4‰ for chalcopyrite (). Sulfides of carbonaceous phyllites along the contact with V2 veins have values of δ34S = + 2.1 to 3.4‰ for pyrite, − 2.9 to + 0.1‰ for pyrrhotite, and + 2.3 to 2.9‰ for chalcopyrite. Pyrite crystals of carbonaceous phyllites along the contact with V3 veins present values of δ34S = − 1.4 to + 6.1‰. In V4 veins hosted in DB1 metamafic dike, pyrite crystals show values of δ34S around + 0.9‰ (Sulfides and sulfosalts in V1 mineralized veins have an average value of δ33S = + 4.2‰ for pyrite, and δ33S = + 3.6 for chalcopyrite (). Sulfides in carbonaceous phyllites along the contact with V2 veins have values of δ33S = + 3.6‰ for pyrite, + 1.5‰ for pyrrhotite, and + 3.4‰ for chalcopyrite. Pyrite crystals formed in carbonaceous phyllites along the contact with V3 veins show an average value of + 5.7‰. In V4 veins hosted in DB1 metamafic dikes, pyrite presents values of δ33S = + 1.0‰ (). Results of mass independent Δ33S for sulfides of the V1 veins hosted in metasedimentary rocks vary from + 0.27 to + 3.46‰ (Data interpretation based on detailed petrography, FI and stable isotope analyses on four major types of quartz ± carbonate ± sulfides ± sulfosalts veins located at the Carvoaria Velha gold deposit, Córrego do Sítio lineament, revealed a complex fluid evolution, presented as follows.Veins represent a complex structural arrangement. They are classified as V1, V2, V3 and V4 vein types (), based on structural and mineralogical observations: V1 veins – quartz-ankerite-sulfides-sulfosalts-gold – parallel to the main regional foliation Sn, and usually mineralized in gold; V2 veins – quartz-ankerite-sulfides – developed along the crenulation cleavage Sn + 1, extensional and rarely gold mineralized; V3 veins – quartz-ankerite – filling Sn + 3 fractures, usually free of sulfides and sulfosalts; V4 veins – quartz-calcite – of restricted occurrence in DB1 metamafic dikes and sills. The V1 to V3 veins crosscut the metasedimentary sequence, are extensional and display no preferential orientation. The V1 vein type corresponds to the earliest vein family and is related to the mineralization event, containing gold that can both occur free and as subordinately included in sulfides. Based on crosscutting field observations, in chronological order V1 is followed by V2 and V3 veins, both of which are sulfosalt free.The V1, V2 and V3 veins contain smoky (QtzI) and recrystallized quartz (QtzII), both analyzed for FI studies. Textural features in QtzI, such as lobate edges, medium-grained crystals, subgrain formation and presence of undulose extinction are suggestive of dynamic recrystallization according to . The QtzI crystals contain numerous FIs (A) and they usually recrystallize to form QtzII, where FIs are rare. In QtzI the number of FIs approximate hundreds, whereas in QtzII they reach perhaps a few dozens. This has been interpreted to reflect the elimination of pre-existing QtzI FIs by their migration that took place during QtzI recrystallization, leaving behind fine-grained QtzII crystals with rare isolated FIs., the usual criteria for distinguishing primary and secondary inclusions may not be applicable in all of the sheared metamorphic rocks, since grain growth and deformation are commonly concurrent processes, which for some minerals, including quartz, continue well beyond the peak of metamorphism. In addition, sheared rocks display frequently large quartz grains that only at the edges are recrystallized but in the core represent the original crystal and by extension the original hydrothermal fluids from which the mineral precipitated. This is the case for the analyzed smoky quartz Qtz I crystals. Furthermore, original quartz crystals are often preserved in pressure shadows around rotated grains.The V4 veins are restricted to the DB1 metamafic dike, presenting diverse texture and mineralogy from V1, V2, and V3 veins. These differences consist of the presence of a single type of quartz with polygonal contacts and incipient deformation, absence of sulfosalts, rare sulfides, and carbonate with a calcitic composition, whereas it is ankeritic in all others (, chlorite-dominated, hydrothermally altered DB1 metamafic dikes seem to demarcate orebodies at the Carvoaria Velha deposit (B), having served as probable barriers for the hydrothermal fluid. However, since the non-deformed, non-mineralized V4 veins are restricted to DB1, and are probably late in relation to V1, V2 and V3 veins, their fluid composition is probably evolved in relation to the fluid responsible for the mineralizing hydrothermal event.The most common sulfide minerals in all vein types are arsenopyrite, pyrite, chalcopyrite and pyrrhotite, presenting diverse textures, and more than one generation (ex. PyI and PyII, ApyI and ApyII), as indicated in section 5.2 of this paper. Microprobe studies show the presence of metallic phases (sulfides and sulfosalts), such as stibnite, berthierite, ullmanite, tetrahedrite, galena, cobaltite and argentopentlandite, commonly overgrowing sulfides (arsenopyrite, pyrite, chalcopyrite and pyrrhotite) (Arsenopyrite crystals may be zoned, with clear irregular portions in both nuclei or rims (), locally enriched in As and depleted in Fe and S. Chalcopyrite may have Fe and Cu depleted rims, and presence of Ni and Co (). Arsenic composition of arsenopyrite crystals in equilibrium with gold and pyrite-pyrrhotite was used as a geothermometer, revealing a range of arsenopyrite temperature of formation from 300–375 °C. This range is interpreted as the temperature for gold mineralization in the Carvoaria Velha deposit.The presence of berthierite associated with gold mineralization in V1 vein type at the Carvoaria Velha deposit differentiates this deposit from the great majority of orogenic gold deposits worldwide (e.g. Hemlo Canada, ). This mineral is mainly associated with pyrite and chalcopyrite (). Gold particles may form inclusions in berthierite. Vein types V2 and V3 are both sulfosalt free, and based on crosscutting field observations; they cut mineralized V1 veins suggesting a close relationship between the presence of sulfosalts and gold precipitation.Based on growth and replacement relationships between sulfide and sulfosalt minerals, an evolution for the mineralizing hydrothermal fluid is proposed. Arsenic and Sb-rich phases suggest that these elements may have been incorporated during the interaction of the hydrothermal fluids with the Córrego do Sítio and Santa Quitéria clastic metasedimentary units. As indicated by , the metallogenetic association of gold-antimony is common in metasedimentary dominant terrains, including Archaen greenstone belts of Canada, South Africa and Australia. In the case of Ni and Co enrichment, it may reflect the contribution of metasedimentary rocks of mafic affinity. Based on the rare earth elements patterns of metaturbidites of the resedimented units belonging to the eastern portion of the Nova Lima Group, where the Carvoaria Velha gold deposit is located, interpret them as having derived from a mixed, mafic and K-rich volcanic source. The presence of Ni and Co also suggests interaction of hydrothermal fluids with the basal sequences of the Nova Lima Group, such as the mafic-ultramafic Quebra Ossos unit, which has its largest expression in the study area when compared to the entire QF.Fluid inclusion assemblages 1 and 2 were established in quartz associated with V1 and V2 veins hosted in metasedimentary rocks, with FIA 1 trapped in both QtzI and QtzII. These are two-phase FIs, with a H2O-CO2 |
± CH4-NaCl composition, and traces of N2, possibly containing other cations than Na+ in solution, such as Mg2 +, Ca2 +, K+ and Fe2 +. The FIs are predominantly aqueous and contain a vapor bubble that generally occupies 5 up to 15% volume of the inclusion cavity, indicating that fluids were homogeneous (miscible) at the time of trapping. Using the criteria by such as, e.g., liquid and vapor-rich fluid inclusions trapped in the same fluid inclusions assemblages at approximately the same temperature, it is clear that there is no evidence of boiling or phase immiscibility in the observed fluid inclusion assemblages. This indicates that the hydrothermal fluids either unmixed at a deeper crustal level, with less dense gas phases disappearing to the surface, or that the fluids did not unmix, i.e., are homogeneous. Based on the microthermometric data (), the hydrothermal fluid is interpreted to reflect at least two evolved stages:an early fluid stage, represented by pseudosecondary FIA 1a trapped in smoky quartz QtzI, of moderate ~ 8.5 eq. wt% NaCl salinity, with an average CO2:CH4 ratio of 5.4, and minimal homogenization temperature of 280 ± 17 °C (a late-stage fluid, represented by: (1) pseudosecondary FIAs 1b, trapped in (partly) recrystallized quartz QtzII (), (2) secondary FIA 1c along trails cross cutting both QtzI and QtzII crystals (), with lower ~ 4.6 eq. wt% NaCl salinity, a lower average CO2:CH4 ratio of 4.9, and a minimal homogenization temperature of 315 ± 33 °C, and (3) locally FIA 1b (n = 5) with homogenization temperatures up to ~ 450 °C, and salinity from 1 to 4.2 eq. wt% NaCl (Taking into consideration pressure values of about 2 kbars obtained for orogenic gold deposits that have similar sulfide-silicate-carbonate hydrothermal alteration assemblages (), a pressure (temperature) correction of Thtot/Td would increase these values in ~ 50 °C, giving a minimum trapping temperature of 330 ± 17 °C for FIA 1a, and 365 ± 33 °C for FIA 1b inclusions. These temperatures are compatible with the range obtained from arsenopyrite geothermometer analyses (It is suggested that FIA 1 represent the mineralizing fluid recorded in quartz of V1 veins, which are related to the first deformational event (Dn event) that was characterized by the Sn foliation. It is interesting to note that fluid inclusions in V1 and V2 veins are similar as far as types and physico-chemical conditions are concerned. This indicate that either: (1) the fluid chemistry did not change during the switch of deformation events, or that these veins belonging to the same deformation event with V1 potentially forming early and V2 late in the deformation event. In either case hydrothermal fluids associated with V1 veins were gold rich, whereas V2 veins only rarely contained gold. The presence of CH4 in FIA 1 from V1 and V2 veins may reflect fluid interaction with Córrego do Sítio and Santa Quitéria carbonaceous matasedimentary wallrocks (cf. ). Fluid-rock reactions could contribute CH4, or other hydrocarbons, and/or N2 (cf. ). The hydrolysis of the carbonaceous matter (2C + 2H2O = CO2 |
+ CH4 or C + 2H2O = CH4 |
+ O2) may have provided CO2 for enhanced carbonate alteration and/or enriched the ore fluid in CH4 |
± N2, as pointed out by for other gold deposits hosted in the Nova Lima Group of the QF region.The addition of CH4 during fluid-rock carbon interaction may have caused some decrease in ƒO2 of the fluid which, as a consequence, destabilized gold-bearing sulfur complexes, liberating S− 2 for the formation of Fe sulfides (Apy, Py, Po etc.), and favor gold deposition (Results of calculated δ18Ofluid values for quartz crystals from V1, V2 and V3 vein types are all similar between + 7.9 and + 13.0‰ (at 280–325 °C) (). Calculated oxygen isotope values for fluids in equilibrium with quartz from V4 veins are lighter, between + 2.6 and + 4.1‰ (). Isotopic δ18Ofluid values of V1, V2 and V3 vein quartz crystals are similar to those of metamorphic fluids (), evidencing the similarity with orogenic gold deposits worldwide, in the + 4 to + 15‰ range (). The V4 vein quartz exhibits the lowest δ18Ofluid values of ~ + 2‰ (), and these are lower than the range of the V1, V2 and V3 vein quartz crystals, suggesting a possible interaction of meteoric waters restricted to mafic DB1 dikes and sills. These dikes may have worked as paths for the percolation of surface waters,Determinations of δ34S for sulfides (pyrite, chalcopyrite and pyrrothite) have a range between − 2.9 to + 6.1‰ (). This large range of values overlap common sulfur reservoirs, and include mantle-derived magmatic rocks (), making it difficult to constrain the original composition of the sulfur source. According to , this relatively wide range of δ34S may be related to recycling of sedimentary materials. In the case of pyrite from V4 veins hosted in DB1 metamafic dikes and sills, the δ34S values are around + 0.9‰ (Results of mass independent Δ33S for sulfides of the V1 veins hosted in metasedimentary rocks vary from + 0.3 to + 3.5‰ (). The presence of positive Δ33S values suggest their sedimentary affinities for sulfur, probably incorporated from the crust (). On the other hand, sulfides of V4 veins, with Δ33S in the range of 0.3 to 0.5‰, indicate its mantle derivation (), as previously interpreted by δ34S. However, as pointed out for the δ18Ofluid data, interaction of meteoric waters cannot be discarded.Sulfides of the V1 veins display a significant MIF effect, which can be compared to values obtained by for pyrites of the Cuiabá gold deposit (U-Pb age of hydrothermal monazite 2.67 ± 0.014 Ga; ) with positive Δ33S values up to + 2.2‰. The incorporation of Δ33S in sulfides from the mineralized V1 veins further suggest that the hydrothermal fluid responsible for gold mineralization at the Carvoaria Velha deposit has interacted with the metasedimentary sequences during its ascending path.Based on detailed mineralogy, geothermometry, fluid inclusion studies, and oxygen and sulfur stable isotopes data reported here, a paleohydrothermal fluid model for the orogenic gold mineralization at the Carvoaria Velha deposit is proposed (Fluid inclusion data for quartz in V1 and V2 vein () suggest that the Carvoaria Velha gold deposit resulted from aqueous-carbonic, low- to medium-salinity (< 8.5 eq. wt% NaCl) mineralizing fluids, at a minimum homogenization temperature of 280 ± 17 °C for gold precipitation, and variable pressures. These results together with fluid isotopic compositions, obtained for V1, V2 and V3 veins (), indicate participation of metamorphic fluids, which are characteristic of worldwide Archean orogenic gold deposits (e.g., ). These fluids interacted with metasedimentary rocks resulting in crustal assimilation of sulfur. On the other hand, the presence of Ni and Co reflects a mafic component contribution to the metasedimentary sequence, such as the mafic-ultramafic Quebra Ossos Group. The fluid-rock interaction yielded also the addition of CH4, causing ƒO2 decrease (). Consequently, ƒO2 variation and pressure fluctuations would have destabilized gold-sulfur complexes liberating S− 2 to form Fe sulfides (Apy, Py and Po, etc.), resulting in gold precipitation (Data obtained for V4 vein quartz associated with metamafic DB1 dikes show a different scenario. They contain (i) aqueous fluid inclusions with the most saline values (average 14.9 eq. wt% NaCl; C); (ii) the lowest δ18Ofluid values of ~ + 2‰ (), suggesting a possible interaction of meteoric waters; (iii) and δ34S values around + 0.9‰ (). We propose that these result from the possible participation of diluted magmatic fluids, since δ18Ofluid of magmatic fluids range from + 4.0 to + 8.0 per mil (The fluid inclusion data (P and T) from the present study place the Carvoaria Velha deposit as having formed at mesozonal crustal levels. Nevertheless, previous studies have indicated that the Au-Sb association points to epizonal crustal level conditions in the formation of orogenic gold deposits (Orogenic and intrusion-related gold deposits commonly can show evidence for fluid immiscibility that can lead to the precipitation of gold (). In the case of the Carvoaria Velha deposit, the lack of evidence for phase immiscibility suggests that the gold precipitation mechanism at the present level of exposure was likely related to cooling of the hydrothermal fluids and/or fluid-rock reactions thereby destabilizing gold-transporting complexes and precipitating gold. Since gold is mainly related to quartz-carbonate-sulfide ± sulfosalts veins, specifically V1, and does not form important replacement-style orebodies, gold deposition must also have resulted from cyclic fluctuations in fluid pressure (Dynamic stability of a size-dependent micro-beamThe effect of variation of the geometrical dimensions on dynamic instability regions (DIRs) of a rectangular cross-sectioned micro-beam with simply supports is discussed in this study based on modified coupled stress theory. A set of linear equations are derived on basis of the Lagrange method and trial series expansions for vertical displacement and rotation of the Timoshenko micro-beam model while longitudinal displacement is neglected due to the stretching effect of the micro-beams mid-plane. The first approximation of the dynamic stability analysis is done by the application of the Bolotin method besides obtaining the Mathieu-Hill equations. The numerical results demonstrate how the cross section's height and micro-beams length are the only effective parameters on DIRs somehow that when the geometrical dimensions are increased the DIRs are going to coincide.The behaviour of micro-elements such as micro-beams which are used for instance as an airbag sensor in the vehicle industry depends on their mechanical properties and dimensions. In Micro-Electro-Mechanical Systems (MEMS) while a structure's geometrical dimensions are miniaturized, the size effect (length scale parameter) has to be brought into account as far as the classical continuum mechanic models are not capable enough to describe this size-dependency effect. In recent years several studies have been done in this field by application of some general theories to describe either micro- or nano-structures performance i.e. Cosserat elastic theory, gradient elasticity theories, modified coupled theory and nonlocal elastic theories () – among a massive number of literature-has used the modified couple stress theory that was introduced by () For modelling the effect of the length-scale parameter and studying the dynamic of micro-elements.A micro-beam is usually loaded with either static or dynamic forces/moments that cause the beam being deformed or vibrated. It is absolutely important to analyze micro-structures’ behaviour for having better knowledge about their performances as it was done by (The motion equation of the micro-beam can be obtained on basis of different models. For example () have used three different models; Euler-Bernoulli, Timoshenko, and higher-order to derive the characteristic equations of the micro-beam. In their study, the solution procedure for a beam with rectangular cross section was highlighted. They just discussed the effect of a cross section's height on the free vibration of the beam.A micro-beam might not be straight and have initial curvature/imperfection respect to its special usage. The dynamic of these structures on basis of the modified couple stress theory was discussed by (). Snap-through buckling of micro-beams with initial curvature on the basis of Euler–Bernoulli beam theory is discussed by () and a new criterion for the snap-through buckling of micro-beams was developed. This study was accurate enough to illustrate the behaviour of an initially curved micro-beam.There are some occasions when a micro-element is subjected to a heating load. These elements' dynamic due to such condition is studied by (). However, the energy dissipation was not considered by () and the numerical Laplace transform was used for solving the obtained partial differential equations. It was also proved that a nonlocal parameter has clear effects on the beam's vibration and elaborated the thermo-elastic stresses, displacement, and temperature related to the ramping time parameter.Free nonlinear vibrations and buckling of laminated composite beams can be analyzed from solving the nonlinear equation which is derived by using He's Amplitude Frequency Formulation (HAFF) and He's Energy Balance Method (EBM) as (). It was shown that the oscillation’ amplitude affects the vibrations of the composite beams in buckling.The micro-structures can be made from novel materials such as functionally graded materials (). They worked on the Timoshenko beam model on basis of the most general strain gradient theory and coupled stress theory to study the static and dynamic behaviour of a micro-beam which is subjected to external loads.Application of modified strain gradient theory (MSGT) and surface stress effects besides the size-dependent influences on the vibration of Timoshenko micro-beams which rests on an elastic foundation with an initial loading is discussed by (). They used the Gurtin–Murdoch continuum method for considering surface stress effects besides governing equations of motion and boundary conditions by Hamilton's principle. Results emphasized that the effect of the pre-stress loading is not too much for higher modes if aspect ratios are high.The influence of length scale parameter on dynamic stability of functionally graded materials Timoshenko beam which its material properties vary in the thickness direction was studied by (). The Mathieu–Hill equation was solved by Bolotin's method. The size-dependency effect on the Dynamic stability of higher-order shear deformable cylindrical with simply supported ends based on the modified couple stress was discussed by () for functionally graded materials micro-shells. The dynamic instability region (DIR) of a simply-supported functionally graded nano-beam under axial and thermal load was investigated for seeking the influence of the static load factor, temperature change, gradient index, nonlocal parameter, slenderness ratio, surface effect and springs constants of the elastic medium (The size-dependency analysis is not limited to beam structures. This study has been extended to the plates and shell as well for instance some of the recent studies are (). Bending, buckling and free vibration problems of functionally graded micro-plates rest on an elastic foundation is analyzed by consideration of efficient size-dependent plate model, which is derived from the strain gradient elasticity and a refined shear deformation theories (). It is elaborated the material length scale parameters causes the stiffness of the FG micro-plate being increased and it causes the plate's deflection and its natural frequency and buckling load are reduced and increased respectively (). They solved the equation of motion of a micro-beam - derived on the basis of modified couple stress theory-analytically to show how the micro-beam frequency is changed respect to the length scale parameter. They have mentioned that the static beam deflections are decreased because of the intrinsic size dependence of materials. Therefore, natural frequencies are increased in consequence.The question arises from the reviewed literature is, if the Poisson's ratio is not ignored how the dynamic instability regions (DIRs) of a micro Timoshenko beam are affected by geometrical dimensions-to-length scale parameter. For having the answer, in this study, a micro-beam with simply supports, axial loading and the modified coupled stress theory is considered, and subsequently, a set of linear equations -Mathieu-Hill equation- is going to be obtained by using Lagrange method for a trial series expansions of the beam's vertical displacement and rotation. The DIRs plots for the micro-beam are illustrated for modified couple stress (nonlocal) and classical theories, and geometrical ratio changes according to excitation frequency and dynamic load ratios.A micro-beam with a rectangular constant cross-section along the entire length -by the width b, height h, and length L - is shown in . The cross section's area is given by A. ρ, E, I are the beam's mass density, Young's modulus and the second moment of inertia respectively. Initial axial load P acts at the end of the beam.The Cartesian coordinate system's origin is set to the right end of the beam. The horizontal axes, x-, passes through the section's centroid. z-represents the vertical axes. The displacement field's components of the micro-beam Here the transversal deflection of the beam in the vertical direction is w(x,t). The longitudinal displacement is neglected according to the stretching effect of the micro-beam's mid-plane. The rotation of the beam along the axis perpendicular to the x-z- plane is given by φ(x,t). The strain energy stored in the micro-beam due to modified couple stress is (In which the symmetric part of the stress and strain tensors are σij and εij, respectively. The deviatoric part of the couple stress tensor is mij, and the symmetric curvature tensor is χij. The strain tensor is defined by,The stress tensor in relation with strain tensor is obtained by (δij is Kronecker delta. λ and μ are Lamé parameters and are defined respect to Young's modulus E, and Poisson's ratio ν,The symmetric curvature tensor is expressed as (The rotation vector is related to the displacement field as (θy=−12(φ+∂w∂x).χxy=χyx=−14(∂φ∂x+∂2w∂x2).The couple stress tensor is defined by (10), in which the length scale parameter is represented by l (T=12∫Vρ(u˙x2+u˙z2)dV=12∫Vρ(z2φ˙2+w˙2)dV=ρ2∫LAw˙2+Iφ˙2dx.In which I=∫Az2dA is the second moment of the area. In (11) the time derivatives are represented by dots. The strain energy of the beam is derived by substituting (4)-(6), (9) and (10) into (2),U=12∫V(σxxεxx+2ksσxzεxz+2mxyχxy)dV=12∫V((λ+2μ)εxx2+4ksμεxz2+4μl2χxy2)dV=12∫L((λ+2μ)Iφ,x2+ksμA(w,x−φ)2+μl2A4(w,xx+φ,x)2)dx.The shear correction factor for the Timoshenko beam is given by ks. It is normally supposed to be 5/6 for rectangular cross-sections. The external work which is done by the axial load, P, on the micro-beam is given by W and computed as (The static and dynamic analysis is going to be done for a simply supported beam, , henceforth the following Fourier series solution as functions in time and periodic in spatial domain which satisfy geometrical and natural boundary conditions are considered (w(x,t)=∑m=1∞wm(t)sin(mπxL),φ(x,t)=∑m=1∞φm(t)cos(mπxL).Here, wm(t) and φm(t) are unknown time-dependent coefficients and are collected in a vector as,Whenever (14) is introduced to (11)–(13) and the Lagrange method is applied, a set of ordinary differential equations that returns the motion's equations of the micro-beam can be derived from the following.This system of equations is expressed in a compact form in a matrix equation by introducing g which are known as the stiffness and geometrical stiffness matrices respectively.Here we suppose that the initially concentrated axial load, P, acts on the beam's end is time-dependent periodic load and it is introduced as;The axial load contains two terms; static, Ps and dynamic, Pd. These components are related to the critical buckling load, Pcr0. The excitation load's frequency is represented by Ω. With introducing two non-dimension coefficients α and β such as the following which are called static and dynamic load ratio respectively,The critical buckling load, Pcr0 is obtained by solving the eigenvalue problem (17) whenever the dynamic term is not considered (static analysis). Introducing the initial time-dependent load, (19) to the motion equation of the beam (17), leads to,This equation is known Mathieu-Hill in the literature. Some methods have been suggested for solving these type of equations, for instance experimental solutions in Bolotin's monograph, Galerkin's method, and Lyapunov's method, asymptotic techniques, perturbation and iteration (). Two aspects were of the most interested to scientists, in this regard; the existence of periodic solutions and their stability. There exists no analytic solution for the motion equation of the periodically excited systems as the second order differential equations with a periodic coefficient, a solution based on () with a period of 2T (a first approximation of the first region of stability) has to be applied for (21). The subsequent approximated time-dependent periodic function is used as a trial solution as suggested by (q¯=∑k=1,3,5,...ak¯sin(kΩt2)+bk¯cos(kΩt2),q¨¯=−(kΩ2)2q¯.Substituting (22) into (21) leads the motion equation of the beam in the form of,(−(kΩ2)2M¯¯+K¯¯+Pcr0(α+βcos(Ωt))Kg¯¯)q¯=0¯,∑k=1,3,5,...[−M¯¯(kΩ2)2+K¯¯+αPcr0KG¯¯](ak¯sin(kΩt2)+bk¯cos(kΩt2))+βPcr0KG¯¯(ak¯sin(kΩt2)+bk¯cos(kΩt2))=0¯.From a mathematical point of view the following trigonometric relations in sine and cosine multiplication can be used to simplify (24) as follows:sin(kΩt2)cos(Ωt)=12[sin((k+2)Ωt2)+sin((k−2)Ωt2)],cos(kΩt2)cos(Ωt)=12[cos((k+2)Ωt2)+cos((k−2)Ωt2)].If (25) being applied to (24), the sine and cosine terms, sin(kΩt2) and cos(kΩt2) shall be separated considering that they are linearly independent mathematical functions. The final form of (24) is:∑k=1,3,5,⋯{sin(kΩt2)[−M¯¯(kΩ2)2+K¯¯+αPcr0KG¯¯]ak¯+12βPcr0KG¯¯[sin((k+2)Ωt2)+sin((k−2)Ωt2)]ak¯+cos(kΩt2)[−M¯¯(kΩ2)2+K¯¯+αPcr0KG¯¯]bk¯+12βPcr0KG¯¯[cos((k+2)Ωt2)+cos((k−2)Ωt2)]bk¯}=0¯.With (k = 1,3) in (26), the first dynamic stability regions () can be found by (27). These equations can be separated into two independent eigenvalue problems regarding the linear independence of the unknown constant which was supposed in (22), ak¯ and bk¯. To simplify the problem it is suggested to use only the first terms as follows:(−(Ω2)2M¯¯+K¯¯+Pcr0(α−β2)KG¯¯)a1¯+(−(Ω2)2M¯¯+K¯¯+Pcr0(α+β2)KG¯¯)b1¯=0.The non-trivial solution of (27) exists if and only if the following determinant is set to be zero that returns two independent equations.It can be illustrated from (28) for which range of the excitation frequency and dynamic load ratio the micro-beam is stable or loses its stability from a dynamic point of view. In this study, the effect of the changing the geometrical dimensions of a micro-beam, , on dynamic stability of the element is illustrated. The non-dimensional ratio of the beam's width, height and length to the length scale parameter are considered. Moreover, the values of the first bending frequency, critical buckling load and dynamic instability regions which are found by classical and nonlocal theories are going to be compared.The numerical calculations were carried out for a micro-beam was made of an epoxy with the following density, Young modulus, Poisson ratio, and length scale parameter is used for computations (ρ=1220kgm3,E=1.44GPa,μ=521.74MPa,l=17.6μm.The variation of the ratio of first natural frequency and buckling load which are computed by using modified couple stress theory over their values that is found by classical theory for a simply supported micro-beam versus geometrical ratios are illustrated in . With respect to the mathematical equations which were derived for the non-dimensional first natural frequency and buckling loads from solving the eigenvalue problem (17), it was found that these equations just depend on the changes in two geometrical ratios, b/l and h/l. The values that predict by modified couple stress theory are going to be closer to ones which are computed from the classical theories. This behaviour has been just elaborated for the first natural frequency of a micro-beam while the element's length changes were only discussed e.g. (Dynamic stability analysis was also done for the micro-beam by using Dynamic instability regions (DIRs) which are V-shaped graphs that indicate the range of excitation frequency ratio, Ω/ω, and dynamic load ratio, see . Inside these borders is called unstable region because of the element – here a micro-beam- loses its stability from a dynamic point of view. However, if the latterly mentioned parameters are selected somehow outside these borders the element motion remains bounded and stable. The velocity of the first time-dependent coefficient of the transversal deflection, dw1/dt, versus w1 is chosen as an example to elaborate the dynamic stability of the micro-beam. the Dynamic instability regions are plotted for classical and modified coupled stress theories. Different values are chosen for the ratio of beam's width to the length scale parameter, b/l. Because the frequency of the beam, ω, which is derived from the eigenvalue problem (17) does not depend on the changes of the beam's width, henceforth no obvious effect on the stability of the beam can be seen by the variation of the beam's width. The frequency of the beam from the nonlocal theory is relatively higher than classical theory, see , therefore, the V-shaped DIRs for the nonlocal theory are located for lower frequency ratio in comparison with classical one.The beams height effect - the ratio of beam's height to the length scale parameter, h/l. - is shown in . It is seen that V-shaped DIRs plots by application of the classical and modified coupled theories are going to be closed whenever the section's height is enlarged. This occurs because the difference between computed values for the natural frequency and buckling load from two theories is decreased. While a micro-beam's height is increased, its natural frequency raises and causes the DIRs plots to shift to the higher ratios of the excitation to the natural frequency., the DIRs are demonstrated for the beam's length effect - the ratio of beam's length to the length scale parameter, L/l. - on the dynamic instability regions of a micro-beam. Enlarging the length of the micro-beam causes the natural frequency of the micro-beam is decreased. In consequence, the DIRs plots are shifted to the lower excitation frequency ratio to the natural frequency. In addition for longer micro-beams, the classical and modified couple theories predict relatively close DIRs diagrams.The effects of the geometrical dimensions ratio to the length scale parameter on Dynamic Instability Regions (DIRs) of a simply supported Timoshenko micro-beam have been discussed. For studying the dynamic stability of the micro-beam with a rectangular cross-section the modified couple stress theory and Lagrange method were applied to a Timoshenko beam model to obtain the micro-beam's equation of the motion. According to the micro-beam's supports type a Fourier series solution as functions in time and periodic in spatial domain that satisfy geometrical and natural boundary conditions were selected for transversal deflection and rotation. Subsequently, the DIRs plots which elaborated the effect of the geometrical dimensions ratio to the length scale parameter on dynamic stability of the micro-beam were illustrated for a specified epoxy as an example.Comparing the natural frequency and critical buckling load of the micro-beam which were obtained by classical and modified couple stress theories proved that their difference just depends on the cross section's height and the element's length. Furthermore, by increasing the latter parameters the difference between the natural frequency and critical buckling load that is determined by these theories are shrunk.The Dynamic instability regions (DIRs) elaborated that the nonlocal theory's plots are located at lower frequency ratios in comparison with the classical theory's plots because the nonlocal theory generally predicts higher values for the natural frequencies in comparison with the classical theory. In addition, the DIRs are going to coincide in consequence because the difference between two theories' natural frequency and critical buckling load are decreased by enlarging the geometrical dimensions. The natural frequency is independent of a beam's width variation hence it causes the dynamic stability of the beam is not affected by its changes. On the other hand, increasing the micro-beam's height shifted the DIRs plots to the higher ratios of the excitation to the natural frequency. However, the DIRs plots were shifted to the lower ratios of the excitation to the natural frequency in consequence of enlarging the micro-beam's length.Pressure-controlled joule-heat forge welding (PJFW)A novel pressure-controlled joule-heat forge welding method to fabricate sound carbon steel joints below the A1 pointA novel solid-state joining method, that we called Pressure-controlled Joule-heat Forge Welding (PJFW), in which electric resistance heat is utilized as the heat source, was successfully developed. Medium carbon steel, S45C, rods were joined using this PJFW method under various conditions. The welding temperature can be determined uniquely by the applied pressure in the PJFW. The fabricated joints show homogeneous temperature distribution and hence hardness distribution along the weld interfaces. A sound S45C joint showing superior tensile properties comparable with the base material was successfully fabricated by providing an appropriate high pressure to lower the welding temperature below the A1 point in order to prevent the brittle martensitic transformation, and applying a sufficiently large faying-surface deformation, not only to introduce significant microstructural refinement and large strains to prevent the softening, but to also sufficiently fragment the oxide layers, generate fresh surfaces, promote their atomic bonding and eliminate weld interface defects.Pressure-controlled joule-heat forge welding (PJFW)Extensive efforts have been made to strengthen structural materials to improve the collision safety of transportation vehicles, and lower their weight to improve fuel efficiency []. Since carbon steels can provide a good strength-ductility combination with low cost by carbon content increasing and appropriate microstructural tailoring, they are considered as promising structural materials for use in the automotive industries. However, for medium and high carbon steels, it is hard to obtain sound weld joints by conventional fusion welding methods due to the brittle martensitic transformation undergoing upon cooling from the high-temperature field (above the phase transformation point, A1) that may cause an occurrence of cracking in the weld zone, and other typical fusion-welding-associated issues, such as coarse columnar grains, high residual stresses, severe welding distortions and solidification voids/defects, which significantly deteriorate the joint qualities []. Solid-state joining techniques with a low welding temperature below the A1 point are, therefore, promising and strongly required to join medium and high carbon steels []. However, the large difference in peripheral velocities between the weld interface center and periphery induces an inhomogeneous heat generation over the weld interface, making the welding temperature and the associated interface microstructure also inhomogeneous and hard to control in the RFW [In this study, a novel welding apparatus was designed in-house for this novel joining method that we named “Pressure-controlled Joule-heat Forge Welding (PJFW)”. Medium carbon steel rods were joined by this method, and the effects of the processing parameters on microstructure and mechanical properties of the joints were systematically investigated in order to obtain a sound carbon steel joint below the A1 point. shows the image of the self-made welding apparatus, which is composed of a power supply (CHUO SEISAKUSHO HVS4E-160-103), an electric servo press (CORETEC FMS100-B), a control panel and a welding unit (both self-made) as magnified in the red dotted rectangle. The power supply is capable of supplying a current up to a maximum 10,000 A at a maximum voltage of 16 V. The electric servo press can provide a maximum load of 100 kN. The welding unit contains two cylindrical jigs having an outer diameter of 60 mm, an inner diameter of 10 mm and a length of 100 mm for the specimen installation. Medium carbon steel, S45C (0.45 wt% C-0.77 wt% Mn-0.23 wt% Si-0.08 wt% Cr-bal. Fe), rods having a diameter of 10 mm and a length of 105 mm were used as the base materials (BM). Before joining, the faying surfaces of the specimens were lathe machined and ultrasonic cleaned in acetone and ethanol. The welding process is schematically illustrated in shows the welding parameters used in the present study in which the current was varied from 3000 A to 4000 A then 5000 A, and the burn-off length was designated as 4 mm, 6 mm, and 7 mm. The applied pressure was kept constant at 250 MPa and the reason for choosing this value is illustrated based on the temperature dependence of the tensile strength of S45C as shown in ]. The tensile strength of S45C decreases with the increasing temperature and it decreases to ~250 MPa when the temperature rises to ~700 °C. Based on these results, it is expected that if a pressure of 250 MPa is applied on the S45C rods during the PJFW process, the welding zone will be plasticized out to form the joint when the temperature increases to ~700 °C, which allows the peak welding temperature not to exceed 700 °C, i.e., below the A1 point. This phenomenon has been reported in our previous study in which the welding temperature in the LFW of S45C plates could be determined by the applied pressure according to its temperature dependence of the tensile strength [The thermal cycles during the PJFW processes were measured by an infrared camera (CHINO CPA-T640) at a 30 fps rate with a reflectivity of 0.78, as illustrated in a. The longitudinal cross-section specimens were prepared from the fabricated joints. These specimens were mechanically polished using waterproof SiC emery papers of up to 4000 grit, followed by an electro-polishing in a solution consisting of 10 vol% perchloric acid and 90 vol% acetic acid at 20 V for ~20 s at room temperature. The electro-polished specimens were then observed by a scanning electron microscope (SEM; JEOL JSM-7001 FA) equipped with an electron backscatter diffraction (EBSD) system to characterize the weld interface microstructure. The Vickers hardness distributions along the weld interface and the longitudinal axis on the longitudinal cross-section specimens, as indicated by the red dotted lines in a, was measured under a load of 0.98 N for a dwell time of 15 s using a hardness tester (FUTURE-TECH FM-800). Tensile specimens having a gauge length of 60 mm and a gauge diameter of 8 mm were prepared from the joints and subjected to room-temperature tensile tests using a mechanical testing machine (SHIMADZU Autograph AG-10 TB) at a cross-head speed of 1 mm/min. S45C BM exhibits a microstructure composed of coarse ferrite and pearlite containing lamellar-shaped cementite, as shown in a shows the thermal cycles measured during the PJFW processes under the different currents of 3000 A, 4000 A, and 5000 A with the constant pressure of 250 MPa and constant burn-off length of 4 mm. The corresponding peak welding temperatures and temperature rising rates from 100 °C to 600 °C are also extracted in shows the weld interface microstructures of the joints fabricated at the different currents of 3000 A, 4000 A, and 5000 A with the constant 250 MPa and 4 mm observed by SEM. All the joints show a microstructure consisting of refined equiaxed ferrite grains and pearlite containing refined ferrite grains and rod- and particle-shaped cementite around the weld interfaces. These results indicate that a dynamic recrystallization occurred around the weld interface, which refined the ferrite grains and fragmented the lamellar-shaped cementite in the pearlite into rod and particle shapes. Defects are observed at all the weld interfaces as circled by the red dotted ellipses. A segment of the weld interface fabricated at 4000 A marked by the yellow dotted rectangle in b′. Both the well-bonded region and non-adhered region are clearly visible at the weld interface. In the well-bonded region, lots of small particles, likely the oxide particles coming from the original faying surfaces, are dispersed consecutively and linearly. Moreover, this particle chain, representing the location of the initial weld interface, is passing through the grains rather than along the grain boundaries. These results infer that the oxide layers on the initial faying surfaces were fragmented into small particles and dispersed by the pressure and the faying-surface deformation to produce fresh metal surfaces on the faying surfaces, then the fresh surfaces were closely adhered and atomically bonded to form a grain boundary under the heat and force; the grain boundary migration then occurred owing to the recrystallization and/or the grain growth at the weld interface, hence leaving the small oxide particles all inside the grain interiors to eliminate the weld interface defects. This solid-state interface joining mechanism has been well demonstrated in our previous study on friction stir welding [It is thus inferred that the faying-surface deformation plays a critical role on the oxide layer fragment and dispersion, the fresh-metal-surface formation, adhesion and atomic bonding, and the weld interface defect elimination during the PJFW process. The burn-off length was accordingly increased to promote the faying-surface deformation and the measured thermal cycles under the burn-off lengths of 4 mm, 6 mm and 7 mm at the constant pressure of 250 MPa and constant current of 3000 A are shown in a. The corresponding peak welding temperatures and temperature rising rates from 100 °C to 600 °C are also provided in b. The thermal cycles for the different burn-off lengths show a similar tendency that the welding temperature increased to an almost constant value of ~700 °C at a similar temperature rising rate of ~120 °C/s, then decreased. These results suggest that the burn-off length did not show an effect on either the peak welding temperature or the temperature rising rate during the PJFW processes. shows the macrographs of the longitudinal cross sections of the joints fabricated at the different burn-off lengths of 4 mm, 6 mm, and 7 mm with the constant 250 MPa and 3000 A. The diameters of the weld interfaces are found to increase from 13.7 mm to 16.3 mm then to 18.4 mm with the burn-off length increasing from 4 mm to 6 mm then to 7 mm, which suggests that the increased burn-off length effectively promoted the faying-surface deformation and enlarged the weld interface area by ~180% by applying the burn-off length of 7 mm compared to the weld interface area fabricated at the burn-off length of 4 mm. displays the corresponding SEM microstructures of the weld interface center and periphery of the fabricated joints. All the weld interface centers show a microstructure composed of refined ferrite grains and pearlite containing refined ferrite grains and rod- and particle-shaped cementite with the absence of martensite, which suggests that the dynamic recrystallization occurred around the weld interfaces for all the conditions below the A1 point. Lots of defects are observed at the weld interface fabricated at the burn-off length of 4 mm as marked by the red ellipses as mentioned above, while the defects are partially suppressed at the burn-off length of 6 mm, then completely eliminated at the burn-off length of 7 mm. It is known that the faying surfaces of the materials were not deformed and closely adhered sufficiently to achieve a strong atomic bonding that caused the weld interface defect formation. By increasing the burn-off length, the faying surfaces were further deformed to further fragment and disperse the oxide layers, produce more fresh metal surfaces, enhance the close adhesion between the faying surfaces, hence finally promoting the atomic bonding and eliminating the defects at the weld interface. In addition, it is noted that the weld interface center and periphery show similar microstructure for each condition, which indicates that the homogeneous heat generation was achieved throughout the weld interface for all the processing conditions. shows the hardness distributions along the weld interface and the longitudinal axis on the longitudinal cross sections of the joints fabricated at the different burn-off lengths of 4 mm, 6 mm and 7 mm with the constant 250 MPa and 3000 A. All the joints showed homogeneous hardness distributions along the weld interfaces, which indicates that the heat generation was uniform along the weld interface regardless of the burn-off length that corresponds to the abovementioned microstructure results. The hardness of the weld interface fabricated at 4 mm was lower than that of the BM, and it increased with the increasing burn-off length; the weld interface fabricated at 7 mm had a hardness comparable to that of the BM. Along the longitudinal axis, the joint fabricated at 4 mm showed a softened zone in the weld interface vicinity, while this softening was gradually suppressed by increasing the burn-off length; the joint fabricated at 7 mm showed the most homogeneous hardness distribution along the longitudinal axis.The microstructure was then examined by an EBSD analysis to further understand these hardness results. shows the EBSD micrographs including inverse pole figures (IPFs) and kernel average misorientation maps (KAMs) of the BM and the weld interface centers of the joints fabricated at the different burn-off lengths of 4 mm, 6 mm and 7 mm with the constant 250 MPa and 3000 A, in comparison with those of the BM. The high-angle grain boundaries (HAGBs, misorientation angle θ ≥ 15°) are indicated by the black lines, while the low-angle grain boundaries (LAGBs, 15° > θ > 2°) are indicated by the red lines in the IPFs. It is noted that the BM has an average grain diameter of ~10.38 μm, while the weld interfaces fabricated at 4 mm, 6 mm, and 7 mm show the average grain diameters of ~3.42 μm, ~2.84 μm, and ~ 1.74 μm, respectively. All the weld interfaces show a microstructure composed of elongated and equiaxed grains. Substructures formed by LAGBs and LAGBs to HAGBs transformation are well recognized in the elongated grains, while almost no LAGBs are visible in the equiaxed grains. These results suggest that the continuous dynamic recrystallization occurred at all the weld interfaces [] and the recrystallization degree increased with the increasing burn-off length that produced the finest grains at the burn-off length of 7 mm. Since all the weld interfaces had the similar thermal cycles, the difference in the microstructure between the weld interfaces is attributed to the different strains due to different burn-off lengths. Although the grain diameter of the weld interface fabricated at 4 mm is the largest among all the fabricated joints, it is still much smaller than that of the BM, which seems difficult to explain the softening that occurred at the weld interfaces. Based on the KAMs, it is noted that large internal strains were initially contained in the BM. These strains were somewhat released at all the weld interfaces, because of the recovery and recrystallization, which hence explains why the softening occurred although the microstructure was significantly refined. The weld interface fabricated at 7 mm thus showed the most homogeneous hardness distribution with no obvious softening or hardening both along the weld interface and the longitudinal axis, which is beneficial for the engineering structural design, and this excellent characteristics is attributed to the balance between the softening owing to the recovery/recrystallization-induced strain release and the strengthening caused by the most significant grain refinement and strain introduction.The tensile properties and the corresponding fractured specimen images of the joints fabricated at the different burn-off lengths of 4 mm, 6 mm and 7 mm, and the constant 250 MPa and 3000 A, in comparison with those of the BM, are hence shown in . The tensile strength and elongation of the joints increased with the increasing burn-off length. The joints fabricated at the burn-off lengths of 4 mm and 6 mm both showed the tensile strength and elongation lower than those of the BM and fractured at the weld interfaces, while the joint fabricated at the burn-off length of 7 mm exhibited a tensile strength and elongation comparable to those of the BM and fractured at the BM site. It is known that the defects and/or non-adhered regions were retained at the weld interfaces at the burn-off lengths of 4 mm and 6 mm because the faying-surface deformation was not enough to sufficiently fragment and disperse the oxide layers, produce fresh metal surfaces, and achieve their close adhesion and atomic bonding, that caused the stress concentrations at the defect sites and the rapid fracture along the weld interface during the tensile loading. Whereas, the increased burn-off length of 7 mm with sufficient faying-surface deformation completely eliminated the weld interface defects and introduced the significant grain refinement and strains to achieve homogeneous hardness distributions both along the weld interface and the longitudinal axis, thereby avoiding the occurrence of stress concentration in the weld zone or its nearby to finally facilitate a fracture in the BM site with a BM-comparable mechanical performance.Based on these findings, it is summarized that the welding temperature can be uniquely determined by the applied pressure, and neither the current nor the burn-off length have obvious effects on the welding temperature during the PJFW of S45C. Since the electric resistance heat is utilized as the heat source, the uniform temperature and hence hardness distribution can be achieved over the entire weld interfaces. A sound S45C PJFW joint having the BM tensile properties with the absence of the brittle martensitic transformation and the formation of the heat-affected softened zone and weld interface defects, can be obtained by providing the approximate high pressure to lower the welding temperature below the A1 point, and applying a sufficiently large faying-surface deformation, not only to introduce significant microstructural refinement and large strains to avoid softening but to also sufficiently fragment/disperse the oxide layers, generate fresh metal surfaces, facilitate close adhesion between the fresh surfaces, promote their atomic bonding and eliminate the weld interface defects. Apparently, this novel PJFW method may also be adopted to other carbon steels regardless of the carbon content and other specimens with other shapes not limited to cylindrical rods.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Microstructure and tensile properties of large-size 7055 aluminum billets fabricated by spray forming rapid solidification technologyIn this study, high-quality large billets of 7055 aluminum alloy were successfully fabricated by spray forming rapid solidification technology. Microstructure observation showed that there were equiaxed grains with the size of about 50 μm in diameter. The dendrite microstructure was suppressed and the undesirable macrosegregation did not exist in the as-deposited 7055 alloys, attributable to rapid solidification effects. The secondary phases were the main η-Mg(Zn,Cu,Al)2 expansion phases and the very small amounts of AlxFe3Cu Iron-bearing phase. As-deposited 7055 billet was subsequently processed by hot extrusion, solid solution treatment at 450 °C/24 h and aging at 120 °C for 12 h. The as-aged alloy was then subjected to tensile testing. The results revealed that yield strength, tensile strength and elongation rate of the alloy reached 608 MPa, 667 MPa and 10%, respectively. After extruding, the observation of the microscopic fracture morphology of as-extruded specimens manifested that fracture mode was the transgranular dimple fracture.For compression dominated airframe structure materials applications, such as the upper wing structure of large commercial aircraft, the requirement of a superior combination of high specific strength, high fracture toughness, improved corrosion resistance and fatigue performance, led to optimization in the composition limits and heat treatment of 7150 Al alloy, and resulted in the design and development of the 7055-T77 aluminum alloy produced by Alcoa in the early 1990’s However, the fabrication process of the 7055 ingot is very difficult because the high alloying element content (Zn > 8 wt%, Cu > 2 wt%) under the relatively lower cooling speed may cause coarse phases, chemical and microstructure segregation as well as severe crack tendency Compared with the traditional forming processes, such as ordinary casting, ingot metallurgy and power metallurgy, the spray forming technology has shown great superiority and potential in the preparation of advanced high-solute Al–Zn–Mg–Cu series alloy In this study, the spray deposition technique was employed to produce high-solute 7055 billets, and alloy composition, microstructure features and related mechanical properties were explored in detail. The formation mechanism of equiaxed grains and microporosities in as-deposited alloys were also discussed. In order to eliminate microporosity defects and improve the mechanical properties, the as-deposited 7055 alloys were performed under the hot extrusions treatment at 450 °C with different area reduction ratio. The effects of extrusion on strength and elongation of the alloys were assessed through ambient uniaxial-tensile tests.The actual composition of the studied 7055 alloy was: 8.31Zn, 2.07Mg, 2.46Cu, 0.12Zr (wt%) and balance aluminum, which was determined by Inductively Coupled Plasma-Atomic Emission Spectrometry (ICP-AES) measurement.The spray-deposition experiments were conducted with a SFZD-5000 type environmental chamber which was manufactured by the Haoran Co. Ltd., Jiangsu, China. During spray-deposition process, the molten metal was atomized by N2 at 820 °C, the distance of atomizing deposition was kept constant at 650 mm. Without homogenization treatments, the as-deposited billets were directly extruded at 450 °C with extrusion speed of 3 mm/s under different extrusion ratio. After extruding, the as-extruded materials were cooled in air. The extruded bar was subsequently solution heat-treated at 450 °C/24 h followed by water-quenching, and artificial aging of the alloy was carried out at 120 °C for 12 h.The microstructures of the alloy were characterized using optical microscope (OM) and scanning electron microscope/energy dispersive X-ray spectroscopy (SEM/EDS). Optical microscopy was performed on an Olympus BH2 microscope. For grain structure examination, samples were etched by Keller’s reagent after ground and polishing. Scanning electron microscopy observation was carried out on the FEI Sirion200 microscope. The specimens preparation for SEM observation were performed similar with OM operations but without etching. In general, backscattered electron (BSE) mode was used in order to get better image contrast. Chemical compositions of various particles in the samples were quantified by EDS analysis.The X-ray diffraction (XRD) experiments were performed on a Japanese Rigaku diffractometer using Cu Kα radiation. The tensile mechanical properties of the alloy were measured by using a MTS-810 test machine at room temperature with a constant crosshead tensile speed of 0.5 mm/min. The tensile fracture morphology was observed also by FEI Sirion200 SEM instruments.a showed a schematic diagram of the spray-forming deposition process and principle. Spray forming technology in the Osprey mode involves sequential stages of metal melting, gas atomization, micro-droplets spraying, deposition and semisolid slurry consolidation. Fortunately, this novel technology can produce near-net shape preforms through the integration of the above stages as one single-step operation naturally. Another important characteristic of spray forming technology is high cooling rate of micro-droplets. It can reach to 104–105 |
K/s b. The billets were 500 mm in diameter and about 1800 mm in length, whose surface was smooth, compact and without cracks. The diameter of billets was uniform from top to bottom. The density of the as-deposited billets has reached to 96.8% of theoretical density measured by displacement method. Such large billets prepared by the spray forming technology, which is feasible to be used in real components rather than experimental studies only in laboratory, has been seldom reported elsewhere.The chemical composition of the fabricated 7055 billet was measured by ICP-AES and listed in . The total amount of alloying element (Zn + Mg + Cu) exceeded 12.8 wt%, and Zn/Mg mass ratio reached to 4.01, while the total amount of impurity elements (Fe + Si) was kept below 0.14 wt%. From the table, the Zinc content was kept on the higher side of the 7055 alloy composition region, while the copper and magnesium were kept at their lower limits in order to allow the alloy to get perfect age hardening effects because of high Zn/Mg ratio showed X-ray diffraction (XRD) pattern of as-deposited 7055 aluminum alloys. The results revealed that there were only η-MgZn2 secondary phase diffraction peaks besides α-Al solid solution peaks. It should be pointed out that S–Al2CuMg phase and T–Al2Zn3Mg3 phase were not detected in the as-deposited microstructures by using XRD measurements, which was different from the result in as-cast 7055 alloys reported by other literature In order to assess the quality of the as-deposited 7055 billets, metallographic examination had been performed by the optical micrograph and the result was shown in a. An equiaxed grain microstructure is distinctly observed in as-deposited 7055 alloys in contrast to a typical dendritic morphology of the primary phase often observed in the as-cast alloys b exhibited the typical SEM–BSE image of the as-deposited Al–Zn–Mg–Cu billets, which was composed of the refined equiaxed grains and secondary phases formed both on the grain boundaries and in the grain interiors. The detrimental coarse eutectic dendrite microstructure in the conventionally processed ingot metallurgy counterpart was suppressed completely in our as-deposited 7055 alloys.Higher-magnification observations of the as-deposited microstructure revealed a large number of white-coarse secondary phases with size of 1–8 μm within the grains (see a). It can be clearly seen that the secondary phases presented various shape, such as particle, rod, needle and square. Most of the secondary phases were distributed relatively uniformly throughout the alloy matrix. On the grain boundary, some of the precipitates were observed to have a discontinuous morphology as illustrated in b. Furthermore, there were some microporosities with the size of about 5 μm found on trigeminal grain boundary occasionally.Microporosity defects were always observed in spray forming as-deposited materials showed SEM images and corresponding energy dispersive X-ray spectrometry (EDS) of as-deposited 7055 alloys. Corresponding EDS data were listed in . In addition to large number of white precipitated phases presented in our as-deposited 7055 alloys, little gray phase can also be found occasionally on the grain boundary.d disclosed that there were Al, Zn, Mg, and Cu elements within white-coarse precipitates. Hence, according to previously mentioned XRD results, the bright phases could be identified as MgZn2. It was obvious that the MgZn2 dissolved lots of the Cu and Al elements, and formed the Mg(Zn,Cu,Al)2 expansion phases. However, there were no Zn and Mg solute in gray coarse phases (see f), the EDS results were 81.53 at%Al, 13.59 at%Fe, 4.88 at%Cu, which was close to stoichiometric AlxFe3Cu Iron-bearing phase in composition. Hence, in the as-deposited alloys, the two types of phases were identified as Mg(Zn,Cu,Al)2 and AlxFe3Cu.It should be pointed out that Cu element was not detected by EDS in the matrix of 7055 alloys (see b). Most of the copper element became enrichment in precipitation phases due to its slower diffusivity. In fact, the diffusion rates of the various solute species were known to be quite different in Al alloys. At 150 °C, taking the data of Refs. a and b offered the typical microstructure of 7055 aluminum alloys after extruding. Optical micrograph and SEM–BSE image magnification were all 500× and the direction of extrusion was marked by arrows on images. The extrusion ratio of this specimen was 6.25. The results showed that, after hot extrusion processing, original equiaxed grains were elongated and fibrous microstructure appeared. Meanwhile, white coarse precipitates was crushed into finer (size less than 3 μm) and realign along the extrusion direction. 7055 aluminum alloy billets were obviously compacted through hot extrusion treatment and microporosities defects within the matrix were eliminated.The characteristics of the spray deposition processes determine its products containing a certain amount of microporosities defects which need plastic deformation (such as hot extrusion) for densification. Actually, plastic-deformation process in the porous material comprises the comprehensive effects of grain displacement, matrix elastic–plastic deformation and the micropores deformation. On the one hand, grains will slide relatively and fill the micropores during the starting of extrusion process. On the other hand, the stress concentration may occur nearby the edge-area of the micropores and make grains deform when the stress surpass the material yield strength. Furthermore, with the increase of deformation, plastic deformation will happen in addition to elastic deformation within matrix grains. Therefore, the deformation undoubtedly causes micropores collapsing and disappears. Relative density of materials after extruding has reach higher than 99.6% of the theoretical value in our experiment. showed the stress–strain curves of spray-deposited 7055 alloys after extruding with extrusion ratio of 6.25 (lightly-extruded) and 39 (heavily-extruded and as-aged) respectively. The tensile experiments were all performed at room temperature (25 °C) with constant strain rate of 0.5 mm/min. For comparison, tensile test of the as-deposited alloys was also carried out and its stress–strain curve was offered. The effects of hot extrusion treatment on the tensile mechanical properties of 7055 alloys were summarized in revealed that the ambient stress–strain curves of as-extruded 7055 alloys might be divided into four areas, i.e. elastic deformation area, yield transition area, plastic deformation area, and necking zone. The ultimate tensile strength was 375 MPa for heavily-extruded sample and 256 MPa for lightly-extruded sample respectively. In contrast to as-extruded samples, the ambient stress–strain curve of as-deposited alloy only presented elastic deformation stage. Materials broke suddenly during the elastic deformation stages and did not appear to yield or plastic deformation phenomenon. The elongation was very small (less than 1%), and the ultimate tensile strength was only 169 MPa. Deformation behavior of as-deposited 7055 alloy was very similar with ceramic-crystal tensile characteristics because the adhesion between grains within as-deposited materials was very weak.As a consequence, the elongation and strength of as-extruded alloy were greatly improved through hot extrusion deformation. Although elongation of as-deposited alloy was less than 1%, after extruding with extrusion ratio of 6.25 and 39, elongation of as-extruded alloys were as high as 12% and 14.5% respectively. Furthermore, due to precipitate-phase hardening effect after aging at 120 °C/12 h, yield strength, tensile strength and elongation rate of the heavily-extruded specimen reached 608 MPa, 667 MPa and 10%, respectively.As is known to all, the tensile fracture surfaces are helpful in elucidating microstructure features on strength, ductility and fracture mode of materials. exhibited typical tensile fracture morphology of as-deposited sample, lightly-extruded and heavily-extruded samples respectively. The fractography of the tensile samples revealed that the microscopic fracture morphology were different due to different fracture mode and the individual features on the surface.Representative fracture features of the as-deposited specimens revealed that its fracture mode was the intergranular brittle fracture. Fracture surface of the as-deposited specimens was very rough and there were secondary cracks (see arrow mark in a). The left-pits of the whole grain were clearly observed in fracture surface after tensile failure. Slight slip trace and very shallow tear edge could be seen under higher-magnification SEM observation.However, the observations of the microscopic fracture morphology of as-extruded specimens demonstrated that fracture mode was the transgranular dimple fracture under uniaxial tensile testing at room temperature, which was shown in b and c. There were many equiaxed dimples and a large number of deep tear edges on fracture surface. The morphology of the fracture contained characteristic of dimples which indicated that the fracture was ductile failure. Generally, there were particles within dimples, and the results of EDS (at%: Mg15.28%, Al35.82%, Cu14.29%, Zn34.61%) indicated that the particle was Mg(Zn,Cu,Al)2 expansion phase. Compared with that of heavily-extruded samples, the dimples of lightly-extruded samples were lager and deeper, which revealed that the ductility of lightly extrusion state samples was better.High-solute large billets of 7055 aluminum alloy were successfully fabricated by spray forming rapid solidification technology. The surfaces of as-deposited 7055 billets were smooth and compact without surface cracks. The microstructure observation indicated that the as-deposited alloys had equiaxed grains with the size of 30–50 μm which was finer than that of as-cast alloys. The detrimental dendrite microstructure was suppressed and undesirable macrosegregation did not exist in our as-deposited 7055 alloys. The distinguished microstructural features of spray forming products were attributed to rapid solidification effects. Thus, spray forming was an effective and efficient technology for fabrication of large-size Al–Zn–Mg–Cu series alloys with high quality.Tensile tests demonstrated that hot extrusion treatments were very suitable for improving the properties of as-deposited materials. Most of microporosity defects were eliminated by hot extrusion in as-deposited materials. After 120 °C/12 h peak aging, the heavily-extruded alloys showed excellent comprehensive performance: high tensile strength (667 MPa), yield strength (608 MPa) and enhanced elongation (10%), which has reached the practical application level. The observations of the microscopic fracture morphology of as-extruded specimens showed that ambient fracture mode was the transgranular dimple fracture.Simulation of dust production in ITER transient eventsDust production from the divertor armour during edge-localised modes (ELMs) has been investigated. Analysis of available experimental data on the dust particle production and the particles distribution on size for the MPG-8 graphite and for NB31 carbon fibre composite (CFC) under the disruption-like surface heat load allowed revealing the unknown mechanical parameters of the NB31 CFC. Using these data the code PEGASUS-3D has been fitted and verified for simulation of the dust production by ELMs. First simulation of the dust production for the ELM of 1 MJ/m2 heat load and 0.5 ms time duration has been calculated.The tritium retention problem is a critical issue for the ITER tokamak performance. According to the rough estimation the maximum tolerable amount of tritium in the ITER vessel is reached after less than hundred shots, but these estimations are based on extremely pessimistic assumptions. Tritium is trapped in co-deposited H3–C layers at the surface of carbon, where it retained in form of various hydrocarbons. Also important for ITER safety, are possibilities of the dust explosion due to chemical reaction with oxygen combined with hydrogen production from steam and spreading of toxic dust. Dust particles surface area can be much larger than the surface of the bulk carbon fibre composite (CFC) armour depending on the particle sizes and the smaller the size the larger the total dust surface area. More accurate calculations for the dust production rate and its distribution on size are needed for realistic estimation of both risks. The carbon dust appears inside the ITER vacuum vessel as a result of damage of the most loaded tokamak part—the divertor armour. Carbon fibre composite of the NB41 grade is now the reference armour material for ITER. The NB41 CFC is the improved NB31 grade with the same fibres structure. It has shown a high thermal conductivity and a tolerable erosion rate appropriate for the tokamak stationary regimes with characteristic temperatures of 1000–1500 K According to the modern understanding of tokamak performance, the most attractive regime for ITER operation is the ELMy H mode. This regime is associated with the edge-localised modes (ELMs) causing high heat flux at the divertor armour under which the CFC armour can crack due to the thermostress, producing a dust of carbon.Theoretical analysis of the erosion mechanism specific for the CFC has been developed earlier using the code PEGASUS-3D Simulation of dust production from NB31 CFC using the PEGASUS-3D code needs information on the matrix structure, and the matrix failure strength and for the failure strength of the CFC fibres. This information is absent and the properties cannot be measured directly. But, these data could be extracted from the results of the available experimental measurements for the dust production under the action of plasma stream. Experimental measurements of the dust particles distribution functions produced under the disruption-like surface heat loads have been done in the MK-200UG and in the MK-200CUSP facilities for NB31 and for the MPG-8 graphite and the results were reported in . The distribution function for the dust particles produced from the NB31 in the MK-200UG and the MK-200CUSP facilities are plotted in The main graphite parameters necessary for the PEGASUS-3D simulations are the mean failure strength for the grains boundaries σb and the mean grain size, λ. For revealing of these values from experiments with the MPG-8 graphite a parametric study has been performed using σb |
= 3–5 × 10−3E∥ and λ |
= 3–8 μm. Here E∥ is the Young’s modulus for graphite crystal in the direction parallel to carbon atom layers. The distribution functions for the dust particles produced under disruption-like surface heat load are shown in . All the calculated distribution functions decreases exponentially with the particle size. But the distribution function for the dust, produced from the numeric graphite sample with smallest mean grain size decreases monotonically, as it has been measured in the experiment. In contrast, the dust obtained from the numeric graphites with larger grains demonstrates pronounced peaks on the distribution function at the positions, which correspond to one, two and three mean grain sizes of the graphite. From this fact the conclusion has been made that the mean grain size of the MPG-8 graphite was 3 μm or even less. Simulation of graphite with smaller λ is difficult from computational point of view. Information on the mean grain size of the MPG-8 graphite is not available, but the grain sizes seen on its surface are approximately 2–3 μm.The parametric study of the dust particles distribution function dependence from the mean grain size λ and from the mean failure strength σb reveal rather strong dependence of the function from the both parameters, see . It is evident that increase of σb on 30% from 3 × 10−3E∥ to 4 × 10−3E∥ drastically decreases the number of dust particles with relatively large sizes 5–10 μm, which corresponds to the dust, composed of 2, 3 and more graphite grains. Increase of λ to 5 μm and σb to 5 × 10−3E∥ leads to erosion of small intergranular particles only. Grains with the mean grain size are not eroded and remain attached to the sample.The parametric study performed allows concluding that the parameters of the PEGASUS-3D code for simulation of the graphite can be reconstructed from the available experimental data obtained in the MK-200UG facility with rather good accuracy. These parameters are σb |
= 3 × 10−3E∥ and λ |
= 3 μm or even less. Comparison of morphologies of the eroded MPG-8 surface obtained in the simulation and in the experiment shown in confirms that the erosion simulation is adequate. The erosion rate for the CFC calculated in the simulation is approximately the same as for the MPG-8 graphite, namely 0.4 μm per shot of the MK-200UG facility.Analysis of the experimental measurements of the dust particle distribution functions for the NB31 CFC under the disruption-like surface heat load in the MK-200UG and in the MK-200CUSP facilities revealed that both distributions are quite similar with the maxima at around 2–3 μm of particle size and with exponential decrease of the particle number with the particle size. The shots of the MK-200UG facility provide 14 MJ/m2 of the surface heat load, 1 MPa of plasma pressure and 40–50 μs time duration, the shots of MK-200CUSP facility—15 MJ/m2 of the heat load, 10 MPa of plasma pressure and 7–12 μs time duration. Comparison of these three distribution functions with that of MPG-8 allows concluding that brittle destruction for the matrix, filling the interspaces of the NB31 fibre structure and for the MPG-8 graphite is universal process, at least concerning the dust of sizes of 1–15 μm with the accuracy of the available data. The only noticeable difference between the MPG-8 graphite and the NB31 CFC is that the debris of NB31 contains particles of much larger sizes up to several hundred micrometers shown in . From these pictures one can conclude that the CFC fibres are eroded as bunches of 100–200 μm length consisting of few fibres stripped off the surrounding matrix.Simulation of the NB31 structure using the PEGASUS-3D code has been performed assuming that the matrix parameters, the mean grain size and the mean failure stress for the matrix grains boundaries are equivalent for the values, calculated for the MPG-8 graphite, λ = 3 μm and σb |
= 3 × 10−3E∥. As a result of similar parametric study, performed for the CFC fibres, the mean failure stress for the PAN fibres has been chosen 12 times larger than the σb value. The simulation of the dust production from NB31 sample has been done only for the region of PAN fibres, which going parallel to the heated CFC sample surface, see The results of simulations for NB31 under the disruption-like surface heat loads are illustrated in (c) and (d). The numerically produced erosion crater and fibre debris are to be compared with the experimentally registered ones illustrated in . Qualitative similarity of the erosion crater and the fibre debris are backed up with the dust particle distributions on size. shows the distribution function for the dust particles produced in the simulation after the time, corresponding to three shots of the MK-200UG facility. It is seen that the distribution function has exponentially decreasing part (sizes less then 10–13 μm) similar for the dust distribution function of the MPG-8 graphite, to compare with The eroded CFC surface morphology after three shots in the MK-200UG facility is shown in (c). It is seen that the main erosion is from the CFC matrix, but the PAN fibres, parallel to the surface eroded too. Erosion of fibres is illustrated in (d), which shows the eroded fibres only. Different gradations of grey colour correspond to different fragments of the fibres. The simulated eroded surface of NB31 is morphologically similar with the eroded surface obtained in the experiment and shown in . Unfortunately large CFC particles was not collected in MK-200UG experiments, but the characteristic length of the fibre debris estimated from the calculations as 60–200 μm, are in agreement with the fibre debris sizes observed in the JUDITH facility, see . Calculated erosion rate for the CFC is approximately 0.4 μm per shot of the MK-200UG facility. Average mass loss for NB31 CFC measured in First simulations for the ITER ELM-like heat loads of the NB31 CFC have been performed using the parameters obtained from the experiments with the disruption-like heat loads of the MPG-8 graphite and of NB31 CFC. The simulation corresponds for the ELM of 1 MJ/m2 total energy load and 500 μs time duration. The results obtained qualitatively are the same as the results for the disruption-like heat loads, but evolution of the CFC debris distribution function needs more time or more ELMs in accordance with the decreased heat load. The dust particle distribution function produced by the ELM is shown in (b). The distribution consists of continuous exponentially decreasing part at small sizes, less then 10–13 μm and of separate debris of larger size up to 25 μm. Total erosion of the simulated sample is a bit less then 1 μm during the ELM of 500 μs, in accordance with the value measured in the QSPA facility Analysing the simulation results one can conclude that noticeable brittle destruction erosion of CFC starts almost simultaneously with vaporization, when the surface temperature reaches some threshold value of approximately Tbd |
= 4000 K. The heat flux reaching the CFC surface after vaporization start is time dependent, but almost does not depend on the external heating flux because of shielding by the vaporized carbon plasma. The time delay of brittle destruction from the start of heating is determined by an approximate formula:where Δt (μs) is the time delay, q (GW/m2) the external heating flux and ΔTbd the difference between Tbd and the initial CFC temperature, ρ the density, C the heat capacity, and κ is the average heat conductivity. With the heat load of 500 μs time duration this corresponds for the erosion start after the total absorbed energy exceeds 0.7–0.8 MJ/m2 in agreement with the measurements in QSPA-T facility Simulation of the carbon dust production has been performed using the PEGASUS-3D code. The experimental data on the MPG-8 graphite and NB31 CFC erosion rates and dust distributions on size measured in the MK-200UG and MK-200CUSP facilities have been used for calibration of the PEGASUS-3D code. Simulations of the dust production from the MPG-8 graphite target under disruption-like surface heat loads in MK-200UG facility have revealed that the PEGASUS-3D parameters for simulation of the graphite are recalculated from the available experimental data with rather good accuracy. Measurements of the dust particles distribution functions for the MPG-8 graphite and for the NB31 CFC under the disruption-like surface heat load in the MK-200UG and in the MK-200CUSP facilities allows concluding that cracking of the CFC matrix and of MPG-8 graphite are the same process, at least for the dust of sizes larger than the graphite grain size. That means that brittle destruction of the matrix filling the interspaces of the NB31 fibre structure could be approximated with the graphite parameters found from the experiments with the MPG-8 graphite with the accuracy of the available data. The only noticeable difference between the MPG-8 graphite and the NB31 CFC is that the debris of NB31 contains much larger particles up to hundreds of micrometers. These large particles are the debris of the CFC fibres, eroded due to their brittle destruction.The results of PEGASUS-3D calculations simulate the experimentally measured data qualitatively – reproducing the eroded surface morphology and eroded fibre debris sizes and shapes, and quantitatively – the erosion rates for MPG-8 graphite measured under the MK-200UG conditions is in a good agreement with the calculated value as well as the size distributions for debris, see . The erosion rate measured for NB31 CFC under the MK-200UG conditions is in a good agreement with the calculated value if one assumes that the that erosion occurs at the PAN fibres regions only and that these regions occupy one quarter of the exposed CFC surface as it is for NB31.The PEGASUS-3D code has been fitted for simulation of the dust production and erosion rate calculation of the NB31 CFC under influence of the ITER ELMs. The code was validated against the available experimental data and shows a good agreement with the experiments in the MK-200UG and MK200CUSP facilities. First simulation of the dust particles production has been performed for the ITER ELM-like surface heat loads using the PEGASUS-3D code with the recalculated parameters. Now the code is fit for calculation of the dust production rate and the size distribution functions for ELMs of different energy size and time dependences of the heat flux.Electron backscattering diffraction (EBSD)Interaction between slip and {101¯2} tensile twinning in Zr alloy: Quasi in situ electron backscatter diffraction study under uniaxial tensile testIn this study, a technique that allows electron backscatter diffraction (EBSD) observation in the same point of interest under uniaxial tensile testing, i.e., a quasi in situ EBSD analysis technique, was developed and performed to investigate the interaction between slip and {101¯2} tensile twinning in a Zr alloy. Both the slip-independent and slip-assisted {101¯2} twins were investigated. The former twin is formed when the global stress surpassed the required critical stress, and the latter one is formed due to the local stress concentration near the grain boundary accumulated in the soft-oriented adjacent grain, although the global stress remains insufficient to activate the twinning. The formation of a slip-independent or slip-assisted {101¯2} twin seems to be closely linked to the crystal orientation relative to the loading direction. It is due to the bimodal basal texture exhibited in the present alloy that the slip-assisted twins can be observed. Furthermore, compared to slip-independent twins, the slip-assisted twinning is more likely to form at a higher strain, because substantial strain accumulation is essential to trigger its activation.Electron backscattering diffraction (EBSD)Zr-based alloys currently have extensive applications in nuclear industry, primarily as core components such as nuclear fuel cladding tubes and grids for nuclear fuel assemblies in various fission reactors []. To manufacture such thin-walled tubes and thin sheets, a series of deformation processes like forging, rolling, and extruding are frequently applied []. In addition, these components suffer from environmental strain during long-term service. For example, the inevitable pellet–cladding mechanical interaction results in strain in the cladding tubes especially under high burn-up conditions; furthermore, in the fuel assembly grid, the deformation induced by fretting wear can occur due to flow-induced vibrations. Therefore, a deeper understanding of the deformation mechanisms in Zr is necessary from the viewpoints of materials' fabrication and service performance.With respect to the plastic deformation behavior of hexagonal-close-packed (hcp)-structured Zr alloys, numerous studies have been performed, and the obtained knowledge on slip and twinning systems during deformation has been well documented []. According to these studies, for the deformation of Zr alloys at room temperature, the most common slip modes in the order of ease of operation are as follows: the {101¯0}<112¯0> prismatic slip, {101¯1}<112¯3> pyramidal slip, and {0002}<112¯0> basal slip. In addition, twinning is required to maintain the deformation compatibility, consisting of tensile twins (TTs) and compressive twins (CTs), depending on whether the c-axis of the crystal lattice is tensioned or compressed; {101¯2}<101¯1> and {112¯1}<112¯6> are frequently reported TTs, and {112¯2}<112¯3> and {101¯1}<101¯2> are CTs. Among these twins, {101¯2} TT is recognized as the most important twinning mode in Zr polycrystals, as it can easily occur due to its relatively low critical resolved shear stress (CRSS), and thus, it can substantially influence texture evolution because this twin significantly reorients the crystal lattice by 85.22° with respect to the <112¯0> [Although much is known about the deformation characteristics in Zr alloys, there is a current lack of studies into the interaction of slip and {101¯2} TT. The competition and coordination between slip and twinning significantly impact the materials' strength and ductility. Thus, the role of dislocation slip on twin nucleation and growth in Zr has been mainly investigated based on the continuum linear elasticity dislocation theory [], and visco-plastic self-consistent (VPSC) polycrystal model calculations []. Obviously, further investigation of the mutual interaction between slip and twinning, particularly by experimental means, is imperative to gain in-depth understanding of the deformation mechanism in Zr alloys. Recently, the application of the (quasi/interrupted) in situ electron backscattering diffraction (EBSD) technique has become a new topic aimed to continuously probe the deformation behavior of materials, and this technique has been utilized to analyze the twinning behavior in hcp metals like Ti and Mg alloys []. However, only very few investigations of Zr and its alloys have been conducted.In this study, we have developed a technique that allows EBSD observation in the same point of interest even after 10% total elongation, i.e., quasi in situ EBSD analysis, which was applied to investigate the {101¯2} twinning behavior in a Zr alloy. The primary objectives of the present study are to figure out the interaction between slip and {101¯2} twinning in the Zr alloy and to elucidate the formation mechanisms of these {101¯2} twins. Both slip-independent and slip-assisted {101¯2} twins were observed, and their relevant formation mechanisms were analyzed based on Schmid's law.Tubular specimens of the Zr-1.8Nb (wt.%) alloy with an outer diameter of 9.5 mm and a wall thickness of 0.55 mm supplied by Mitsubishi Nuclear Fuel Co., Ltd., were used as the experiment materials in this study. This alloy is one of the candidate materials developed as advanced fuel claddings for next-generation light water reactors (LWRs) in Japan []. 0.38-mm-thick plates were obtained by cutting and cold-rolling the tube, and were finally annealed at 853 K for 24 h under vacuum (at pressures < 5 × 10−4 Pa). Small specimens for uniaxial tensile tests were prepared with the gauge length of 5 mm and width of 1.2 mm. The length direction was set perpendicular to the rolling direction (RD). Uniaxial tensile tests were conducted at room temperature using a Shimadzu AG-X Plus apparatus at a strain rate of 10−3/s. shows the schematic illustration of a stress-strain curve of the specimens subjected to a regular uniaxial tensile test and interrupted tests. The stress-strain curve for the regular test indicates that the present material has a rather high ductility, allowing a total elongation of ∼28%. The yield strength at 0.2% strain and ultimate tensile strength (UTS) were measured as 386 and 434 MPa, respectively. Besides the regular tests, the interrupted tensile tests were performed successively at strains of ∼2% and ∼10%. Immediately after the interrupted tests, the microstructure in the same region was characterized by the EBSD technique using a JXA-8530F field emission gun SEM with OIM (v7.3b) software, to acquire detailed crystallographic information concerning the grains. The region for EBSD analysis was roughly at the center of the surface of the gauge section. shows the EBSD inverse pole figure (IPF) map and (0001) pole figure of the Zr-1.8Nb alloy plate. It can be noted that the microstructure fully recrystallized after the annealing and contained equiaxed grains with a low dislocation density. The average grain size was measured as ∼4 μm, using a linear intercept method. A majority of the grain boundaries (GB) were found to be high-angle GB (15°–180°), while the rest were the low-angle GB (5°–15°). None of the most common twin boundaries ({101¯2}, {112¯1} TTs and {112¯2}, {101¯1} CTs) was present. b presents the crystal texture, which is the typical bimodal basal texture found in various cold-rolled and annealed Zr and its alloys []. The (0001) pole figure reveals that c-axes preferentially tilt ∼20° from the normal direction (ND) towards the transverse direction (TD) of the plate, indicating that the basal poles are oriented mostly along ND but rarely along RD and TD.The results of the quasi in situ EBSD observation are shown in a–c, which present the IPF maps analyzed in the same region in non-deformed, 2%, and 10% strained conditions. The application of tension loading along the TD resulted in most of the grains becoming elongated in the TD and shortened in the RD, which is particularly obvious for the 10%-strained specimen (c). In parallel with the change in the grain shape, strain accumulation simultaneously occurred within the grains. This phenomenon can be discerned in d–f, which show the misorientation profile evolution along the arrows in grain #1 (G1), grain #2 (G2), and grain #3 (G3). In these grains, the misorientation basically increased with deformation. In comparison with G1 and G2, the misorientation increment in G3 was much greater, revealing a more active dislocation movement within this grain.It is worth noting that a newly formed fine lamella sandwiched between G1 and G2 was observed in c. Further analyses on the 10%-strained and fractured specimens were conducted to identify this newly formed grain, as shown in a shows the IPF map of partitioned grains of G1, G2, and the newly formed lamella. According to the misorientation profile, this lamella exhibited misorientation angles of ∼85° and ∼90° with a rotation axis along <112¯0> in the case of G1 and G2, respectively, which reveals that G1 has a more consistent axis angle pair to {101¯2} TT, relative to the slightly different G2. This discrepancy is due to the low-angle (∼5°) GB between G1 and G2, which is also inferred from c. A similar analysis was conducted on the fractured specimen (at a strain of ∼28%), and the result is shown in . Most of the grains are highly strained in the fractured specimen, as revealed by the intragranular color gradient (a and c). In addition, the presence of twin-like lamellae was observed in grains marked as G4–6 (c). Corresponding misorientation profiles along the black arrows are respectively shown in b and d, and the enlarged G4–6 and G7–9 are respectively presented in . The misorientation angle between the lamellae and neighboring matrix in G4–9 was revealed to be ∼85°/<112¯0>, so these lamellae were identified as {101¯2} TT. With respect to the presence of {101¯2} TT in the fractured specimen, it is reasonable to conclusively consider the lamella sandwiched between G1 and G2 in 10%-strained specimen as {101¯2} TT as well. To summarize, only {101¯2} TT was observed even after fracture, and the quasi in situ observation results imply that the occurrence of {101¯2} TT started at a strain <10%.{101¯2} twinning occurs due to shear stress on the {101¯2} twinning plane and along a specific shear direction of <101¯1> as the twinning direction. Theoretically, there are six equivalent twin variants within this twinning system due to the existence of six possible equivalent {101¯2} crystallographic planes, i.e., {101¯2}[1¯011], {1¯012}[101¯1], {011¯2}[01¯11], {01¯12}[011¯1], {1¯102}[11¯01], and {11¯02}[1¯101]. From the characteristic misorientation angle of ∼85° with respect to the <112¯0> rotation axis (according to the EBSD data), it is possible to identify them as {101¯2} twins. However, it is insufficient to distinguish the variants consistently and directly due to the limitations in the determination of both misorientation angle and axis from EBSD data []. To further reveal the characteristic features of the twins, the activated variant twin was identified using a twinning rotation method [], which has been applied frequently to Mg and Zr alloys []. Specifically, the activated twin variant is determined by applying the six possible twinning rotations to the experimentally obtained matrix grain orientation and then selecting the one that most closely matches the experimentally observed twin orientation. shows the identification result of twin variants in G2 and G4–9, where θ is the misorientation angle between the predicted and experimentally observed twin variant. The twin variant with the minimum misorientation angle was determined to be the activated one and denoted in bold in . Note that the twin formed between G1 and G2 was analyzed using the orientation parameter of G2, as G2 had a more consistent axis angle pair relative to G1 (see The origin behind the phenomena studied in the present work is discussed based on Schmid's law, given as: σ=τCRSS/m, where σ is the critical stress required to activate a certain deformation system, determined by τCRSS and m, which are respectively the CRSS and Schmid factor (SF) of a certain deformation mode in the grain of interest. The CRSS values for the various deformation systems are provided from references: 153±30, 532±58, and 204±66 MPa for <a> prismatic, <a+c> pyramidal, and <a> basal slip [], respectively, and 165 MPa for {101¯2} TT []. These deformation systems were selected because they are considered as the most common deformation modes at room temperature in Zr alloys, as reported in earlier studies []. The SF for slip systems is calculated using orientation coordination from EBSD data, and for {101¯2} TT, the SF is calculated using the crystallographic indices of the activated twin variant, as shown in In G1 and G2, the <a> prismatic slip shows a low value of SF, i.e., 0.18 and 0.10, whereas in G3, the value is much higher. On the contrary, the SF of {101¯2} TT shows higher values in G1 and G2 compared to G3. After collectively considering the CRSS, the calculated critical stress for each deformation mode indicates that the <a> prismatic slip in G3 is activated when the strain is in the range of 2–10%, whereas {101¯2} TT has not been triggered, as the actual stress is lower than the required critical stress. Conversely, in the case of G1 and G2, the critical stresses of {101¯2} TT and <a> prismatic slip are respectively lower and higher than the actual stress at 10%-strain, indicating the activation of TT and the inactivation of the <a> prismatic slip in these grains. Thus, the occurrence of {101¯2} TT in G1 and G2 follows Schmid's law well. This interpretation also accounts for the phenomena described in d-f. The greater intragranular strain accumulation in G3 than in G1 and G2 results from the more active primary prismatic slip in G3. In addition, it is believed that a higher stress concentration is preferentially exerted near GB, due to the strain accommodation between the adjacent grains with different orientations []. Such high stress near the GB probably accounts for the formation of {101¯2} TT along the low-angle grain boundary between G1 and G2. Unfortunately, EBSD maps could not be successfully obtained with the further growth of this TT, due to the poor quality of the data caused by the high strain.The formation of {101¯2} TT, which was observed in the fractured specimen, appears to be different from that of G1–2. From b-c, the SF distribution and calculated critical stresses in G4–9 are not similar to those in G1–3; the critical stresses of the <a> prismatic and <a> basal slips are lower than that of {101¯2} TT. UTS of 434 MPa is still not enough to reach the critical stress for {101¯2} TT in all these grains; hence, twinning is not expected to be triggered. Therefore, the appearance of twins indicates that Schmid's law is not applicable in these grains. This discrepancy is presumed to stem from the mutual relationship between the crystallographic orientation of the grain and loading direction. Schmid's law is reported to be applicable for analyzing {101¯2} twinning in Mg alloys when the tension/compression deformation is parallel/perpendicular to the c-axis []. A similar phenomenon might occur in the Zr alloy. As seen for the hexagonal unit cells in a, the c-axes of G1 and G2 are near-parallel to the loading direction. This near-parallel relationship enables a consistent interpretation of the {101¯2} TT behavior, as shown in a. On the contrary, for G4–G9, their c-axes are more deviated from the parallel to the loading direction, which presumably results in the appearance of twins despite the fact that the global critical stress required for twinning has not been reached in those grains.After excluding the factor of internal crystal orientation, the extrinsic factor, e.g. the adjacent grains, is taken into consideration to elucidate their formation mechanism. The SFs of the primary <a> prismatic slip in the surrounding grains of G4–9 are then summarized and indicated, as shown in a–b and d-f. It thus becomes apparent that these {101¯2} TT containing grains are neighbored by grains with a high SF for the <a> prismatic primary slip, indicating the activation of prismatic slip within these grains. Accordingly, dislocation formation dominates during deformation, and intragranular strain accumulates steadily with increasing strain. The constantly accumulated dislocations would then impinge the GB, resulting in local stress fluctuation near the GB. As long as the local stress at the GB surpasses the required critical stress of {101¯2} TT in the adjacent grain, twinning will be triggered, leading to the appearance of a {101¯2} twin in the grain on the other side of GB, although the global stress remains insufficient to activate the twinning. This assumption of strain accumulation near the GB has been experimentally confirmed in a strained Zircaloy-4 alloy [b–c); the grain with a high SF of 0.49 in the primary prismatic slip is firstly deformed in the mode of the prismatic slip, by which dislocations accumulate and induce the impingement onto the GB adjacent to G6. When the local stress on the GB reaches the critical stress for {101¯2} TT, the twinning nucleates and propagates to relieve the stress concentration. c shows the kernel average misorientation (KAM) map of G6 and its adjacent grain. Obviously, there is a much higher strain at the GB, indicating the accumulation of high local stress there. Further, the formation of a twin can greatly accommodate the stress accumulated at the GB. Due to this accommodation, local stress concentration is not observed in G6, and the strain level within the twin becomes relatively lower compared to that in the adjacent matrix. This slip-assisted twin mechanism can be further confirmed on account of the fact that the twin in G6 seems to nucleate from the GB (where the adjacent grain exhibits a SF of 0.49 in the <a> prismatic slip) and to grow across the whole grain.On the basis of the above discussion, the mechanism of slip-independent and slip-assisted {101¯2} TT in the present Zr-Nb alloy is schematically illustrated in . The slip-independent twin, i.e., the {101¯2} TT forms when the global stress surpasses the required critical stress based on Schmid's law; the c-axis of the hcp lattice in such grains tends to be parallel (or at least close) to the tension direction, which results in a low SF in the primary prismatic slip but a high SF in {101¯2} TT. In other words, {101¯2} TT is favored relative to slip under this crystal orientation. With increasing strain/stress, twinning is firstly activated when the required critical stress is obtained, prior to slip dislocations. In contrast, for the slip-assisted twin, it seems likely to occur in the grains whose c-axes are more deviated from the parallel to the tension direction. The crystal orientation under such conditions generally gives rise to a lower SF in {101¯2} twinning. One more prerequisite required in the slip-assisted mode is that at least one adjacent grain should exhibit a soft orientation for slip, i.e., a high SF in the prismatic slip. After deformation starts, the prismatic slip will be firstly activated in the adjacent grain. As deformation proceeds, the dislocations increase and continuously pile up near the GB, gradually resulting in the formation of a local stress concentration near the GB. When the local stress reaches the critical stress for {101¯2} TT in the neighboring grain, twinning will be triggered to accommodate the local strain, although the global stress remains insufficient to activate the twinning.) in the current Zr-Nb sheet is considered to play an important role in forming such slip-assisted {101¯2} twins. For grains with their c-axes close to the ND of the sheet (e.g. <20°), the primary slip is favored when being tensioned along the TD; however, for grains with their c-axes more inclined from the ND to RD (e.g. >40°), the preference of the primary slip is somewhat weakened when the tension direction is parallel to the TD. Within the present specimen, most grains are of the former type, while there is also a certain number of grains of the latter type. The co-existence of these two types of grains in the present specimen ensures the occurrence of slip-assisted twins. Conversely, as revealed in b, the number of grains whose c-axes are perpendicular to the ND of the sheet (i.e., c-axis of the lattice is parallel to the tension direction) is limited, and {101¯2} TT is much more favored than slip under the same tension. This indicates that the presence of slip-independent twins is improbable in the current textured specimen. Moreover, in comparison to the slip-independent twin, the slip-assisted twin is more likely to be formed at a higher strain because a substantial strain accumulation is required for the activation of twinning. This explanation rationalizes the fact that the slip-independent twin was present in the 10% strained specimen, whereas the slip-assisted twin was only observed in the fractured (28% strained) specimen.To clarify the interplay between slip and twinning, in general, data sets ought to be as abundant as possible, due to the complex boundary conditions in practical materials when being strained. For example, Abdolvand et al. recently studied the grain neighbor effects in polycrystalline Zr after examining >8800 grains with the use of three-dimensional synchrotron X-ray diffraction [], and Tomé et al. statistically examined the nucleation and growth of twins in Zr based on EBSD measurements performed on hundreds of grains, as well as the twin transmission effects between neighboring grains []. Although relatively limited numbers of grains/twins were investigated within this study due to the unfavorable orientation-loading condition for {101¯2} tensile twinning as explained previously, the reliability of the proposed mechanism could be further verified from the good consistency with numerous previous studies. In a similar structured α-Ti, it has been experimentally confirmed that the prismatic slip in a soft-oriented grain can stimulate {101¯2}<1¯011> twin formation in neighboring hard-oriented grains, as determined by a combination of backscatter electron images, orientation maps, and in-situ far-field three-dimensional X-ray diffraction analyses by Wang and Bieler et al. []. Further, it has been revealed from a spatially resolved crystal plasticity fast Fourier transform calculation that the twin-resolved shear stress is relatively higher at the grain boundaries where the twin embryo forms [], agreeing well with the KAM analysis in -c. Thus, despite the limitation in the insufficient number of analyzed grains, the results from the present study are reliable and able to provide supporting evidence for better understanding the interaction between slip and {101¯2} tensile twinning in polycrystalline Zr alloys.In summary, a quasi in situ EBSD observation under tensile tests was performed to understand the interaction between slip and {101¯2} tensile twinning behavior in a Zr-Nb alloy. Two types of formation mechanisms, namely slip-independent and slip-assisted twinning, were elucidated. The role of slip in the nucleation of {101¯2} twins probably depends on the parallel relationship between the crystal orientation and loading direction. Moreover, a higher strain is more likely needed for the formation of slip-assisted twins relative to the slip-independent ones. The findings of this study will supplement existing knowledge on polycrystalline Zr alloy deformation, especially considering that as one of the pivotal deformation systems in Zr, the occurrence of {101¯2} tensile twins will substantially affect material properties such as strength, ductility, and texture.Microstructure and mechanical properties of Al2O3/Ni compositesNi-coated Al2O3 powders were prepared by the heterogeneous precipitation method. After hot-pressing at 1300–1450 °C and 20 MPa, the density of homogeneous Al2O3/Ni composites ranges from ∼98% (NA4) to ∼94% (NA8.5) of the theoretical density. Examination by transmission electron microscope (TEM) and scanning electron microscopy (SEM) shows micrometer-size Ni grains to be located at the triple junctions, and with increasing Ni content, the fracture mode of Al2O3/Ni composites to change from intergranular mode to transgranular mode due to the thermal stresses. The strength and toughness of composites was much higher than that of the dense monolithic Al2O3. The strengthening and toughening mechanisms of the composites with respect to the microstructure are analyzed.It is well-accepted that the fracture toughness of the brittle Al2O3 ceramic can be increased through the incorporation of ductile metal In recent years, coating as a processing aid for ceramic particles has been investigated. It not only improves the green density and sintered activity Ni-coated Al2O3 powders in the desired composition were prepared using Al2O3 with average diameter of 0.35 μm (Shanghai Songjiang Fertilizer, Co., China), Ni(NO3)2·6H2O (analytically pure) and NH4HCO3 (analytically pure) as starting materials. Ni(NO3)2·6H2O, Al2O3 and 0.5 wt.% (equivalent to Al2O3 weight) polyacrylic acid as dispersant were firstly mixed in distilled water by ball milling for 48 h. Next, NH4HCO3 solution of 1.0 M was added dropwise to the homogeneous slurry obtained above under vigorous stirring. Its reaction was following equation The precipitates were not dissolved in ammonia solution . The resulting powders were sintered at 1300–1500 °C for 0.5 h in an argon atmosphere with an applied pressure of 20 MPa. Pure Al2O3 ceramic was prepared at 1450–1550 °C for 0.5 h under the same rest conditions as the composite. The sintered bodies were cut to dimensions of |
mm. The samples are designated as NAx, where x is Ni contents.X-ray diffraction (XRD) patterns were obtained at a scanning rate of 4°/min with 2θ range from 10° to 70° using a fully automated diffraction (Rigaku RAX-10, Japan) with Cu Kα (0.15406 nm) radiation. A transmission electron microscope (TEM) (Model JEM-200CX, JEOL, Tokyo, Japan) was utilized to investigate the particle size, shape of the coated powders and composite. Fracture surfaces were examined by scanning electron microscopy (SEM) (EPMA-8705QHz) to investigate fracture model and grain size. Bulk density was measured by the Archimedes method. Three-point flexural strength measurements were carried out with a span of 20 mm and a crosshead speed of 0.5 mm/min at room temperature by an Instron-1195 Universal Test machine. Fracture toughness, KIC, was determined using an indentation technique with a Vickers indenter (AKASHI) using 98 N load. The formula used for calculating KIC was expressed as KIC=A(E/H)1/2(p/c2/3) is the variation of relative densities for Al2O3/Ni composites containing different Ni content with hot-pressing temperature. The relative density of the samples enhances with increasing sintering temperature. When Ni content is relatively lower (for example NA4, NA6.5), the samples attain the highest relative densities of 98.6% at 1450 °C. In contrast to monolithic Al2O3 ceramic with the same density, sintering temperature decreases by about 100 °C. It can be seen from that there are lot of pores in sintered sample at 1450 °C, and few in sintered sample at 1550 °C. The reason is that Ni particles (∼20 nm) in the coating layer are very fine, and the activity of sintering is largely enhanced. When Ni content is relatively higher (for example NA8.5), the samples attain the highest relative densities of ∼94% at 1400 °C. Above 1400 °C, the relative density of the samples containing high Ni content is lower than that of the samples containing low Ni content. Al2O3 is not wetted by solid or liquid Ni ) when the composites are cooled down from a sintering temperature. The more Ni content is high the more the interface of Al2O3/Ni is big, and then the more the produced pores are many (). This phenomenon can be observed from . As a result, the relative density of the samples containing high Ni content is relatively lower. is thermally etched photos of the Al2O3/Ni composites containing different Ni contents. The grain structure of matrix phase and inclusion are noted. Because the atomic number of Ni is far higher than Al2O3, the scattering contrast results in a white feature for Ni grains and gray for Al2O3 grains. The micrographs clearly reveal that Ni grains are agglomerated, located at the triple junctions, and homogeneously dispersed in Al2O3 matrix. On the other hand, some exaggerated Al2O3 are found. However, TEM () indicates some small Ni particles of less than 0.3 μm exist in the exaggerated Al2O3. In an early stage of sintering, the separation between grain boundary and small inclusions can take place as the velocity of grain boundary is much faster than that of inclusions, therefore, small Ni particles can be swallowed in the matrix grains during matrix grain growth The average size of Al2O3 and Ni grains are given in ). The average grain size of monolithic Al2O3 is much bigger than that of Al2O3/Ni composites, which shows that the introduction of Ni particles can restrain the growth of Al2O3 grains. However, with increasing Ni content, the average size of Ni and Al2O3 grains become big, namely, effect on restraining the growth of Al2O3 grains becomes weak. This may qualitatively be explained by Zener’s model where r and f are grain diameter and volume fraction of the second phase, respectively. Zener’s model indicates that when grain diameter of the second phase is constant, the grain size of the matrix decreases with increasing volume fraction of the second phase. Thus, the introduction of Ni particles can restrain the growth of Al2O3 grains. And when f is constant, the grain size of the matrix becomes big with increasing the size of second phase. In this paper, with increasing Ni content, nanoNi grains agglomerated and grown during sintering. Therefore, effect on restraining the growth of Al2O3 grains becomes weak. is SEM micrographs of fracture surface of the samples with different Ni content. It can be observed that the fracture mode of monolithic Al2O3 is basically intergranular fracture, and the fracture model changes from intergranular model to transgranular model as Ni content is enhanced. The change in fracture mode can be explained on the basis of thermal stresses. When the composite is cooled down from a sintering temperature, the thermal stresses are generated in the composite produce due to thermal coefficient mismatch between the ceramic matrix and inclusions. Since the thermal expansion coefficient of Ni (15×10−6 |
°C−1) is larger than that of Al2O3 (8.4×10−6 |
°C−1), according to the theory proposed by Selsing The strength and the toughness of the composites are shown as a function of Ni content in . Each point in the figures represents the average value of four specimens. The error bars indicate one standard deviation. Compared with the dense monolithic Al2O3, Al2O3/Ni composites show a marked increment in both strength and toughness. For example for NA4 sample, the strength and the toughness increase by 15–28%, respectively.According to Griffith theory, the fracture strength (σf) of brittle material is expressed as the following equation:). Therefore, the higher strength of the Al2O3/Ni composite is attributed to the decrease in grain size of the Al2O3 matrix (see ). When Ni content is higher, the decrease in the strength of the composites results from the decrease of the density of the composites is SEM micrograph showing the crack propagation from the polished surface of the composite. Except for the crack deflection toughening, the crack branching and crack bridging (arrow) are contributed to the increment of the fracture toughness.NanoNi coated Al2O3 composite powders were successfully synthesized by the heterogeneous precipitation method via using Al2O3, Ni(NO3)2·6H2O and NH4HCO3 as starting materials, subsequently, which were sintered by hot-pressing at 1300–1500 °C for 0.5 h to obtain Al2O3/Ni composites. The density of the composites was found to range from ∼98% (NA4) to ∼94% (NA8.5) of the theoretical density.Microstructure studies found that Ni grains are agglomerated, located at the triple junctions, and homogeneously dispersed in Al2O3 matrix. With increasing Ni content, the fracture mode of Al2O3/Ni composites changes from intergranular model to transgranular mode due to the thermal stresses.In contrast to the dense monolithic Al2O3, the addition of nanoNi can reduces sintering temperature, decreases in grain size of Al2O3 matrix, and shows a marked increment in the mechanical properties. The increment of strength is due to microstructural refinement. Toughness enhancement is attributed to crack deflection, crack branching and crack bridging.Mixed whey protein isolate/gellan gum gelsSerum release boosts sweetness intensity in gelsThis paper describes the effect of serum release on sweetness intensity in mixed whey protein isolate/gellan gum gels. The impact of gellan gum and sugar concentration on microstructure, permeability, serum release and large deformation properties of the gels was determined. With increasing gellan gum concentration the size of the pores present in the protein network, the permeability and the serum release increased, as well as the Young's modulus, the fracture stress and the fracture strain. Increasing the sugar concentration induced an increase of the pore size, but resulted in a decrease of permeability and serum release. The addition of sugar resulted in gels with a higher Young's modulus and a lower fracture strain. This effect was more evident at higher gellan gum concentrations. By changing the protein concentration of the gels, a set of samples was prepared exhibiting constant large deformation properties but varying in serum release and sugar concentration. Serum release significantly boosted sweetness intensity. For example, the sweetness scores for gels with 12% serum release were the same as for gels with 2% serum release but 30% higher sugar concentration. The results indicate that serum release is a tool to compensate for the loss taste intensity related to the reduction of sugar and salt in gelled foods.Iso-sweetness curve: for protein gels, an increase in serum release by a factor 6, from 1% to 6%, allows a reduction of the sugar concentration by 30% without effects on sweetness perception.Mixed whey protein isolate/gellan gum gelsConsumers are highly sensitive to small variations in sweetness. This has been established for several different foods, ranging from sugar solutions to cookies (). Therefore, reduction of sugar when developing light foods remarkably affects the taste of the products, and this can have repercussions on the choice of the consumer. Successful strategies to reduce sugar aim at maintaining the taste of the reformulated product unvaried as compared to the original food.Semi-solid gelled food products are generally complex products containing different ingredients, such as proteins, carbohydrates and fats. Mixed or composite products comprising both proteins and polysaccharides are sensitive to phase separation, either on a macroscopic or on a microscopic level (). Recent studies on cold-set whey protein isolate (WPI)/polysaccharide mixed gels showed that minimal variations in the type and concentration of the polysaccharide resulted in a wide ranges of microstructures (). In these gels only the protein phase was in the gelled state. The concentrations of the polymers added to the protein dispersions were below the gelling concentration. Therefore, between the protein structures originated as a consequence of phase separation only aqueous solutions were present. The empty spaces in which these solutions were contained were described as pores. For these cold-set mixed WPI/polysaccharide gels a clear relationship was described between the molecular properties of the polysaccharide and the microstructure of the mixed gels. This relationship between ingredients and microstructure allows precise control over the mechanical properties of the final product. The microstructure of these mixed gels strongly affected their large deformation and sensory properties (Taste–texture interactions have been studied in polymer solutions and pourable model foods, as well as in gelled systems. An inverse correlation between viscosity of fluid foods and taste intensity has often been reported (). In hydroxyl propyl methyl cellulose (HPMC) solutions an increase of the polymer concentration (i.e. an increase in viscosity) resulted in a decrease of the perceived sweetness (). The same effect of polymer concentration on saltiness was observed for HPMC and λ-carrageenan solutions (). In solutions of random-coil polymers a suppression of taste perception with increasing polymer concentration is reported to start at the critical concentration at which coils overlap and entanglements occur (). The reduced rate of transport of tastants from the interior of the sample, where they cannot be perceived, to the exterior appears the dominant factor in the suppression of taste perception in these systems.Gel formation suppresses mixing between thickener and tastants molecules and thus inhibits migration of tastants to the taste buds. Therefore, in gels an extreme suppression of taste perception would be expected. An inverse correlation between taste intensity and the hardness of soft solid foods has been reported (). In κ-carrageenan and gellan gum gels containing both sucrose and aspartame as sweetening agents, a decrease of sweetness perception was observed with increasing polymer concentration (i.e. with increasing Young's modulus and fracture stress) (The occurrence of serum release from WPI/polysaccharide gels is of importance with respect to the perception of tastants (). Serum release can be related to the juiciness perception in fruits and vegetables, as well as in meat products and meat replacers (). The phenomenon of serum release observed by van den Berg was mainly dominated by the microstructure of the gel, whereby gels with bicontinuous microstructure showed the highest amount of serum release upon compression. As tastants need to be dissolved in saliva before they can be perceived by the taste buds, serum release is likely to improve this process and enhance the perception of tastants in gelled products.We hypothesize that serum release from cold-set mixed gels can improve and enhance the perception of non-volatile tastants, such as mono- and disaccharides. In order to study this hypothesis, a set of mixed WPI/gellan gum gels with controlled serum release, constant large deformation properties and different sugar concentrations was prepared. With these gels a quantitative descriptive analysis (QDA) study was carried out.Powdered whey protein isolate (WPI, Bipro™) was purchased from Davisco International Inc. (La Sueur, MN, USA). Gellan gum (low acyl, Kelcogel F) was kindly provided by CP Kelco Inc. (Lille Skensved, DK). Glucono-δ-lactone (GDL) was kindly donated by Jungbunzlauer (Marckolsheim, France). Sucrose, glucose and fructose were obtained from local shops. All materials were used without further purification. All samples were prepared with demineralised water.Mixed WPI/gellan gum gels were prepared by acid-induced cold gelation. Reactive WPI aggregated were prepared incubating a 9 wt% WPI solution at 68.5 °C for 2.5 h. After this heat treatment the aggregates dispersion was cooled with tap water to approximately 18 °C and immediately used for gel preparation. Stock solutions of gellan gum (0.6 wt%) were prepared by stirring the polysaccharide in water for 2 h and subsequently heating at 80 °C for 30 min under constant stirring. After heating, the polymer solution was cooled to approximately 18 °C with tap water. For gel preparation, the WPI aggregate dispersion was mixed with varying amounts of the gellan gum solution and with varying amounts of different sugars (sucrose, glucose, fructose) and diluted with water to a typical protein concentration of 3 wt%. To induce cold gelation GDL (0.25 wt% for gels with 3 wt% WPI) was added. An incubation at 25 °C for 17 h followed. The final pH of the gels was about 4.8. The preparation of the gels for the sensory study was optimised to obtain constant large deformation properties for all samples by varying the protein concentration. The composition of the samples with constant large deformation properties is reported in The pH of the gels was measured with a Knick Portamess 911 pH pH-meter (Knick Elektronische Messgeräte, GmbH & Co. KG, Berlin, Germany), by inserting the electrode directly into the gel and waiting until a constant value was reached. The measurement was performed at room temperature. The experimental error was 0.05 pH units.Uni-axial compression tests were performed approximately 20 h after preparation on cylindrical gel pieces of 25 mm height and 25 mm diameter. An Instron 5543 machine (Instron International Ldt., Edegem, Belgium) equipped with a plate–plate geometry was used. In order to prevent friction between the plates and the samples, the plates were lubricated with a thin layer of paraffin oil. The measurements were performed at room temperature, at a constant deformation speed of 1 mm/s and up to a compression strain of 80%. The true strain (ɛH), i.e. the absolute deformation of the specimen, and the true stress (σt), i.e. the overall stress acting on the sample during deformation, were calculated as follows:where H0 is the initial height of the specimen, H the actual height during deformation, F the force measured during compression and A the corresponding cross-sectional area of the specimen. For each sample at least 5 gel specimens were analysed.The serum release was measured as described by using uni-axial compression tests with cylindrical gel specimens of 25 mm height and 25 mm diameter. The compression tests were performed with an Instron 5543. A strain rate of 0.004 s−1 was applied in all cases. For these measurements, no paraffin oil was used to lubricate the Instron plates. The gel specimens were placed in a Petri dish in order to collect the exuded serum. The collected serum was weighted and the serum release was calculated as follows:where Ms is the mass of the exuded serum and Mg is the mass of the gel before compression. The measurements were performed at least in duplicate. The serum obtained from gels containing sugar was collected and the sugar concentration was determined. For the determination of the sugar concentration in the serum released from the gels, the HPLC method with refractive index detection described by was used, without further treatment of the samples.The effect of the ratio WPI/gellan gum and sucrose concentration on gel permeability were determined as described by Verheul (). Gels were prepared in glass tubes with an inner diameter of 3.7 mm and a length of 25 cm. The tubes were open at both ends. The height of the gels in the tubes was approximately 3 cm. The tubes were individually filled with a dispersion of 3 wt% WPI aggregates containing varying amounts of gellan gum solution and sucrose, and the appropriate amount of GDL. The ends of the tubes were closed with rubber tips and the tubes were incubated at 25 °C for 17 h. After gelation 7 tubes per type of gel and 5 reference tubes without gel were put in a measuring vat made of Plexiglas at 20 °C. For measurements of gels prepared without sugar, the vat was filled with demineralised water. For gels containing sugar, a sugar solution with the same concentration as that of the sugar in the gel was used. To wet the surface two droplets of the measuring solution were put on top of each gel. Changes in the level of measuring solution on top of the gels were measured in intervals of 30 min by means of a cathetometer. The permeability coefficient, B (m2), was calculated by the following equation:where h∞ is the average height (m) of the measuring solution in the reference tubes, ht1 is the height (m) of the solution in the tube with gel at t1, ht2 is the height (m) of the solution in the tube with gel at t2, η is the viscosity of the measuring solution (Pa s), H is the height (m) of the gel, ρ is the density of the measuring solution (kg/m3), g (m/s2) is the acceleration due to gravity and t1 and t2 (s) two subsequent measuring times (taken from the start of the measurement). The end value of the permeability coefficient was the average of values measured at least at 8 different times. All experiments were performed in triplicate. The values reported are the average of the three different experiments.Samples for microstructural analyses were stained with Rhodamine B (0.2 wt% solution; 10 μL per mL sample) to visualise the protein phase. CLSM images were recorded at room temperature on a LEICA TCS SP5 Confocal Laser Scanning Microscope, equipped with an inverted microscope (model Leica DMI6000) and with a set of four visible light lasers (Leica Microsystems (CMS) GmbH., Mannheim, Germany). A Leica objective lens of 63× magnification was used (HCX PL APO 63×/1.20 W CORR CS). The excitation wavelength was set at 488 nm. Digital image files were acquired in 1024 × 1024 pixel resolution representing an image size of 0.246 mm × 0.246 mm at zoom 1.The sensory characteristics of the gels were investigated with the use of a sensory panel trained according to the principles of Quantitative Descriptive Analysis (QDA) (). The panel consisted of 12 females aged between 22 and 49 and with above-average scores on all selection tests. These tests included tests of odor identification, odor memory, and verbal creativity, and a series of texture tests in which the ability of the panelist to assess fattiness, roughness, and particle size was measured. All panelists had previously been trained for the assessment of the sensory properties of mixed WPI/gellan gum gels. Panelists were seated in sensory booths with appropriate ventilation and lighting. The products were assessed semi-monadically in duplicate on visual analogue scales. The presentation order was randomly assigned per panelist. Acquisition of the panelist's responses was done by computer using FIZZ software (Biosystemes, 1998). In 4 sessions of 2 h the panel were presented and trained with a set of 12 gel samples. During these training sessions descriptive attributes were generated that were used to profile the gels (The relationships between sensory attributes and gel samples characteristics were summarized using Principal Component Analysis (PCA) (Unscrambler 7.5, Camo Inc., Corvallis, U.S.A). PCA facilitates the identification of attribute synonyms and covariate attributes. Relationships between specific attributes were statistically modeled using Partial Least Squares Regression or PLSR (Unscrambler Vs. 7.5, Camo Inc., Corvallis, U.S.A). The effects of changes in ingredient composition on individual sensory attributes were analysed using a factorial ANOVA (SPSS, SPSS Inc, Chicago, U.S.A.), carried out on the raw sensory data. Because the ANOVA was carried out on the raw sensory data, it was possible to carry out tests of significance for all effects.To study the effect of serum release on sweetness perception in mixed WPI/gellan gum gels the optimisation of a series of samples with the same serum release and large deformation properties at a certain sugar concentration was required. In order to achieve this goal, the effect of sugar concentration on serum release and large deformation properties was studied at different gellan gum concentrations and for different sugars, i.e. sucrose, glucose and fructose.At the deformation speed used for the compression tests the Young's modulus (the slope of the fracture curve at 10% strain), the fracture stress and fracture strain increased with increasing gellan gum concentration (A). These effects are in agreement with the results of . The addition of sugar resulted in an increase of Young's modulus and a decrease of fracture stress and fracture strain (B). This effect was more evident at higher gellan gum concentrations. At higher sugar concentrations the above described effect of gellan gum on large deformation properties was smaller.The effect of gellan gum concentration on serum release was in agreement with the data published by ). Sugar caused a decrease of the serum release. This effect was larger at sugar concentrations higher than 10 wt% and was the smallest for fructose (). Because of its higher relative sweetness, fructose allows to obtain samples with a larger sweetness range and with a smaller effect on serum release and large deformation properties. Therefore, it was decided to use this sugar for the optimisation of samples for the sensory study.To explain the effect of gellan gum and sugar on serum release, the microstructure of gels with increasing gellan gum and sugar concentration was studied. As previously reported (), increasing the gellan gum concentration in a range 0.025–0.04 wt% caused a remarkable change in the microstructure of the gels (). The pores present in the protein network can be described as the phase volume of the immiscible polymers. At a gellan gum concentration of 0.025 wt% the microstructure of the gels was protein-continuous. Increasing the concentration of gellan gum to 0.04 wt%, i.e. increasing the ratio between the phase volume of the polymer and that of the protein, the microstructure became bicontinuous. In the curve shown in the observed change in microstructure corresponded to a gradual increase in serum release. A further increase in gellan gum concentration had only a slight effect on both pore size and interconnectivity (). At gellan gum concentrations higher than 0.04 wt% the curve shown in levelled off. Gellan gum concentrations higher than 0.065 wt% resulted in macroscopic phase separation: a layer of gellan gum appeared on the top of the gel. The microstructure of gels in which macroscopic phase separation occurred was comparable to that of gels with 0.065 wt% gellan gum. Also an increase in sugar concentration caused an increase of the pore size of the gels. The protein beams of gels with sugar appeared thicker than those of gels without sugar. The presence of sugar, affecting both the viscosity and the osmolarity of the system, could have repercussions on the relative phase volume. Furthermore, sugar could have a delaying effect on the gelation of the protein phase, resulting in a longer time for phase separation to occur. the permeability coefficient is plotted as a function of the gellan gum concentration for gels with different sugar concentrations. For the gels without sugar, an increase of the permeability coefficient by a factor 8 was observed when increasing the gellan gum concentration from 0.025 to 0.040 wt%. The presence of sugar contrasted the effect of gellan gum on permeability. For the gels with 20 wt% sugar, the mentioned increase in gellan gum concentration resulted in an increase of the permeability coefficient only by a factor 3.The concentration of sugar in the exuded serum was in good agreement with the sugar added to the gel (results not shown). This clearly shows that no retention of sugar within the gel matrix occurred.Varying the protein concentration by keeping a constant protein/polymer ratio allowed to modulate the mechanical properties of the gels without affecting the serum release. This finding, together with knowledge on the effect of sugar and gellan gum on serum release and large deformation properties allowed to optimise the preparation of a set of samples for the sensory study with constant large deformation properties and almost equal serum release as compared to the sample without sugar (). The chosen protein/polymer ratio's resulted in samples with serum release in a range 2–40 wt% (D). Increasing the fructose concentration caused a slight decrease in serum release (D). Since the difference in serum release between gels with different gellan gum concentration was still large, this effect of fructose was found acceptable.During the training sessions the QDA panel generated 23 attributes describing odor (1), taste (4), mouthfeel (11), after taste (4) and after feel (3) sensations (). These attributes were used to rate 12 mixed WPI/gellan gum gel samples with increasing serum release (from 2 to 40 wt%) and fructose concentration (from 0% to 12 wt%). The PCA plot was described by two main axes, one (PC1) related to texture and going from slippery, crumbly, firm and resilient to rough, separating and water release, the other (PC2) related to taste and going from bitter to sweet (). Gels with increasing serum release moved along PC1 and were perceived as less slippery, firm and resilient and more rough and separating. Gels with increasing sugar concentration moved along PC2 and were perceived as more sweet.For sensory attributes of particular interest, the relation between serum release, sugar concentration and score of the individual samples was investigated. The scores for the mouthfeel attribute water release increased for gels with higher gellan gum concentration and slightly decreased with increasing sugar concentration (A). The observed trends for this attribute were remarkably similar to those of the measured serum release (D). Small variations in serum release related to an increase in fructose in gels with constant gellan gum concentration were clearly perceived by the panel.The decrease of the score for the attribute resilient observed with increasing serum release (i.e. increasing gellan gum concentration) (B) is in agreement with the decrease in recoverable energy reported for these gels with increasing gellan gum concentration (). The decrease of the scores for the attribute firm observed with increasing serum release was surprising (C). As a matter of fact, the stiffness and the strength of the samples as obtained by compression measurement were very similar for all samples. Furthermore, for gels with higher serum release the stiffness and the strength of the gels are supposed to increase during deformation (i.e. as the serum exudates from the gel matrix). A hypothetical explanation for this phenomenon could be an interaction between serum release and firmness perception. The presence in the mouth of larger amount of serum after mastication was related by the panel to lower gel firmness.The scores for the attribute sweet were significantly higher for gels with higher serum release (D). Increasing the serum release from 2 wt% to 35 wt% induced an increase of the scores for this attribute by 30–45%. The increase of the scores was relatively larger at lower sugar concentration. In the relation between increase in serum release and decrease in sugar concentration at constant sweetness is shown. When increasing the serum release by a factor 5–6, the same sweetness can be perceived with 30% less sugar.In mixed WPI/gellan gum gels with a low protein concentration, varying the protein concentration by keeping a constant protein/polymer ratio allows to modulate the mechanical properties of the gels without affecting the serum release. The modulation of the serum release in food gels appears to be a powerful textural tool to enhance sweetness. Using this approach allows to reduce sugar levels without loosing taste intensity.Investigation into the shear stress, localization and fracture behaviour of DP600 and AA5182-O sheet metal alloys under elevated strain ratesShear tests were performed at strain rates ranging from quasi-static (0.01 s−1) to elevated rates (600 s−1) considering DP600 steel and AA5182-O aluminum alloy sheet at room temperature. The shear specimen due to Piers et al. [J. Peirs, P. Verleysen, J. Degrieck, Experimental Mechanics, 52 (7), pp. 729–741, 2012] was scaled (reduced in size) to perform high strain rate shear testing. In situ digital image correlation (DIC) techniques were employed to measure the strains in the experiments and methods are proposed for characterizing the local strain within shear bands. Using the DIC strain measurements along with finite-strain theory and the logarithmic objective stress rate, a simple methodology was developed to obtain the work hardening response to large strain levels using only shear and tensile experiments. At lower strains, the DP600 shows positive rate sensitivity while the AA5182 exhibited limited sensitivity as strain rate increases. At equivalent strains greater than approximately 20%, the DP600 and AA5182 alloys demonstrated a reduced work hardening rate at elevated strain rates. For both alloys, the strain to localization (using the Zener-Holloman criterion) and subsequent fracture strain, measured using the DIC technique, decreased with strain rate in shear loading, but increased under uniaxial tensile loading. Microscopic assessment of fractured DP600 specimens was also performed using measurement of grain boundary rotation to determine local strains at fracture corresponding to length scales below the DIC measurements. The local strains at final failure are much higher and reveal an increase in the shear fracture strain with strain rate, in contrast to the trends based on the DIC analysis.The forming and subsequent crash of automotive sheet metal components involves large plastic strains, high strain rates and adiabatic heating that softens the material and potentially alters its strain rate sensitivity and fracture behaviour. As the automotive industry has moved towards the adoption of ultra- and advanced high strength steel and aluminum alloys for vehicle light weighting, the finite-element codes for computer aided engineering (CAE) of forming and crash require increasingly accurate material models to work within the limited process windows of these higher strength, lower ductility alloys. In particular, the material hardening response at large strains and strain rates should be well characterized along with the material high rate fracture behaviour under stress states ranging from shear to equal biaxial tension. Traditionally, material characterization at elevated strain rates has been performed using uniaxial tensile tests with miniaturized geometries A complementary test for material and fracture characterization at large strains and elevated strain rates is a simple shear test that unlike the tensile tests, does not develop a through-thickness necking instability at low strains and for which deformation remains planar as simple shear does not promote thickness strain (plane strain in nature). In addition, the lack of a necking instability enables deformation to be linear and proportional until fracture so the fracture strains can be implemented within a stress-state dependent fracture locus as in a modified Mohr–Coulomb approach Torsion tests are not suitable for sheet materials; therefore, various simple shear test geometries have been developed Shear testing of sheet under dynamic strain rates were initially performed by Campbell and Fergusen DP600 and AA5182-O sheet alloys are selected for the present work since they are commercial automotive alloys and also allow comparisons with the recent high rate characterization of these alloys using uniaxial tension tests reported by Rahmaan et al. The objective of the current work is to investigate shear behaviour of automotive alloys at high strain rates, as well as further develop experimental analysis procedures for shear characterization at elevated strain rates to obtain the hardening response up to large strain levels. In concert with DIC strain measurements during the experiments, microscopic examination of the extent of grain rotation due to shear at low and high strain rates is also performed to ascertain the effect of strain rate on the extent of localization in the strain field. The ability of stereo DIC was evaluated to measure local shear strains to failure at high rate and compared to the macroscopic or continuum-level strains with measurements of the microstructure. This study provides insight into the differences between two strain measurement techniques and how to account for this variability in future CAE models where the shear failure strain appears to be changing with strain rate. The objective of this work also includes the development of a formal experimental methodology to experimentally determine the stress-strain behaviour to large strain levels using the shear tests without inverse modelling techniques. In order to adapt the mini-shear specimen This section opens with a review of the fundamentals of simple shear deformation for finite-strain conditions. These concepts and the equations presented herein are subsequently applied to determine the stress state and local strains within the shear specimens and to develop a methodology to convert the measured shear stress-strain response to the equivalent true stress-strain data needed to characterize hardening behaviour to large strain levels. In addition, the magnitude of the normal stress components developed under large-strain simple shear deformation are also calculated and shown to be small relative to the shear stress component.In continuum mechanics, a shear state is often described in terms of simple shear deformation. The deformation gradient, Fij, for a simple shear condition in the x1−x2 plane can be written as: |
For proportional, simple shear loading, the logarithmic strain tensor, εij, and rotation tensor, Rij have been derived by Zhou et al. The maximum shear strain for the strain tensor in can be expressed as a function of γ as: |
ε12max=ε112+ε122=ln(γ2+1+γ22)=sinh−1(γ2)The principal strain components, ε1-3, can be determined by: |
, for a simple shear test for material characterization using digital image correlation (DIC) for strain measurement, the reported metric should be the major principal strain () or equivalently, the maximum shear strain (), that are valid for large deformation and are independent of the yield function (unlike an equivalent strain measure). The use of the applied shear strain, ε12, will be valid for small strain levels as significant normal strain components will develop with deformation (see |
). As mentioned above, equivalent strain definitions are dependent on adopted yield functions, for instance, for the popular von Mises criterion, the equivalent strain in simple shear can be expressed as: |
It is worth noting that there is some degree of rotation of the principal directions in simple shear () that should to be considered for constitutive characterization of anisotropic materials; however, for the relatively isotropic materials considered in the present study, the influence of rotation of the principal directions is expected to be negligible.The stress tensor in simple shear loading to finite strain also contains both shear and deviatoric components in plane stress loading as: |
in which the normal stresses are related through the constraint that there is no hydrostatic stress in shear loading: σ11+σ22+σ33=0. For low to moderate strains, the normal stresses are assumed to be negligible relative to the magnitude of the applied shear stress and the stress tensor reverts to its familiar, infinitesimal form The principal stress components in simple shear loading contain only two unique stress components, σ11 and σ12, as shown in , and the principal stresses (σ1−3) can be determined by: |
a major challenge in shear testing is the calculation of the normal stresses that develop at large strain; however, for low to moderate strains, the normal stresses (σ11 or σ22 in ) are expected to be negligible relative to the magnitude of the applied shear stress and the principal stresses can be expressed as a function of the shear stress because σ1,2=±σ12 and σ11 ≈ 0. Note that the local DIC logarithmic strain measurements are valid for large strains and no assumptions are required to obtain the principal strains. However, for constitutive characterization of materials in shear, it is often assumed that the normal stresses in |
remain negligibly small compared to the shear stress.To quantify the shear strain level at which point the normal stresses are no longer negligible under simple shear loading, an analytical stress integration based on the measured strain history can be performed to establish experimental guidelines for the range of deformation that the normal stresses in the stress tensor () can be approximated as zero. For simplicity, a fictitious power-law hardening flow stress model is assumed, as in , that can be generalized to a broad range of materials by using n-values between 0.1 (moderate hardening) and 1.0 (linear hardening): |
where, σ¯ is the flow stress, εp is the equivalent plastic strain, and σy is the initial yield stress. It was assumed that σy and K are equal to 300 MPa and 500 MPa, respectively. In addition, a perfectly plastic condition (σ¯=σy) was also considered. Note that the linear form of Hooke's law was adopted in the elastic region and the associative flow rule was assumed to calculate the direction of the plastic flow. The yielding response of the material was described by the isotropic Hosford yield criterion |
where, a is the homogeneity exponent and three different values of a=2 (von Mises), a=6 (typical for BCC materials), and a=8 for (FCC materials) were considered in the present study. For simple shear calculations to finite strain levels, the logarithmic objective stress rate was adopted since it is an exact work-conjugate pair with the Cauchy stress and the shear experiments use the logarithmic strain measures from the DIC strain measurements. Furthermore, the logarithmic spin tensor, Ωijlog, of Xiao et al. [ΩLog]=γ˙4(44+γ2+γ4+γ2sinh−1(γ/2))[010−100000]The logarithmic spin tensor of Xiao et al. In order to examine the evolution of magnitude of the normal stress components with deformation, the analytical results are presented in the form of normalized stress (σ11/σ12, see ) with respect to the major principal strain, as shown in . It can be seen from the figure that for different hardening and homogeneity exponents, the normal stresses remain quite small (below 0.4% of the shear stress) for major principal strains of up to 100%. Therefore, assuming that normal stresses are negligible in simple shear appears to be valid for the range of deformation commonly encountered in forming and crashworthiness applications.Although the magnitudes of the normal components of the strain tensor can be written in terms of the shear deformation (), as shown above, the magnitudes of the normal components of the stress tensor are related to the adopted constitutive model (hardening model and yield function) and form of the adopted objective stress rate. The requirement to assume a constitutive model and objective stress rate complicates the experimental determination of the stress tensor to large strain levels as only the shear stress, σ12, can be determined experimentally from the applied load and gauge area as σ12 |
= F/A; however, it was shown in that the magnitudes of the normal stresses remain negligibly small compared to the shear stress. Therefore, the stress tensor can be approximated as: |
Without DIC strain measurement, the analysis is limited to small strains (less than 20%) where the normal strains remain small and the infinitesimal strain theory is valid where the strain tensor, principal strains, and von Mises equivalent strain can be written as: |
However, using full-field DIC strain measurements, the applied strain tensor along with its incremental form are known throughout the entire deformation process so there is no need to assume that the strain tensor has the form of where the normal strains are negligible. The DIC measurements can confirm that simple shear loading conditions are achieved during the test provided that ε1=−ε2 in the gauge section. When this condition is met, a plane stress state is obtained where the principal stresses will be equal and opposite (σ2=−σ1,σ3=0), and the following procedures can be used to calculate the elastic/plastic strain components, plastic work per unit volume and the work-conjugate equivalent plastic strain without assuming a yield criterion.The logarithmic strain tensor can be decomposed into elastic and plastic tensors: |
where the principal elastic strains can be determined from Hooke's law for isotropic elasticity as: |
Since, σ11/σ12 ≈ 0 is valid, the principal elastic strain () for the entire deformation process can be approximated to first-order accuracy as: |
This approximation will introduce less error into the plastic strain tensor than the assumption of a rigid-plastic material where ε ≈ εp, and also avoids the calculation of σ11/σ12. Then the incremental and total plastic work per unit volume (wp) can be readily determined from plastic work equivalence: |
and simplified for simple shear using the constraints, σ3=0, σ2=−σ1, dε2p=−dε1p to obtain the ratios between the plastic strain increments (flow rule) and the stress (yield criterion) as |
Note that the definition of the plastic work in Eq. (22) assumes that the directions of the principal stress and principal plastic strain increments are aligned so that the work balance is strictly valid for lower strain levels and approximate for finite-strains. By neglecting the normal stress components which remain small relative to the shear stress, the work conjugate equivalent plastic strain increment can be thus be estimated without adopting a yield function using dεeqp=2(σ12σeq)dε1p=2(σ12σTensile)(dε1−dσ122G) |
where the ratio, σ12/σTensile, is the ratio between the shear stress and the equivalent stress obtained from a uniaxial tensile test at the same plastic work. This stress ratio can be determined experimentally at each plastic work level until necking occurred in the tensile test. The ratio σTensile/σ12, can be assumed to be constant for materials without evolving anisotropy and then be used to compute the equivalent stress as: |
It is worth noting that, although the choice of the uniaxial tensile direction in is not crucial for isotropic materials, care must be taken for selection of the tensile orientation for anisotropic sheets. As mentioned earlier, shear loading leads to two equal and opposite principal stresses that are oriented 45° with respect to the maximum shear plane. For instance, a shear test with the applied load in the 45° orientation leads to a tensile principal stress in the rolling direction (RD) and a compressive principal stress in the transverse direction (TD) or 90° to the RD be selected as the RD. Similarly, when experimental shear data in the RD direction is available, the tensile direction selected should be the diagonal direction (DD) or 45° to the RD.Thus, both the work conjugate equivalent plastic strain as well as the flow stress to large strain levels can be determined experimentally through only the shear experiment and a corresponding uniaxial tension test. Alternatively, if uniaxial tensile test data as a function of plastic work is unavailable and the yield function is also unknown, then an estimate for the shear stress ratio can be obtained by assuming the material to be isotropic at the shear location of the yield surface and using the non-quadratic Hosford yield criterion |
where, a = 2 provides the von Mises yield criterion whereas a = 6 is recommended for BCC materials and a = 8 for FCC materials. The resulting shear stress ratios for 2, 6 and 8 are approximately 0.577, 0.558 and 0.545.The DP600 steel and AA5182-O aluminum alloy sheets considered in this work have the same nominal thickness of 1.5 mm. The chemical compositions of the materials are shown in . Specimens were machined along the sheet rolling direction (RD). The same lots of materials investigated herein have also been characterized by the present authors under uniaxial tensile loading The mechanical properties of the DP600 and AA5182-O sheet metal alloys are presented in . The ultimate tensile strength (UTS) and the ultimate elongation (UE) strain of the materials shown in correspond to the rolling direction (RD). The general stress-strain behavior for both materials are similar along the rolling (RD), diagonal (DD) and transverse (DD) sheet orientations correspond to the last measured values. The reader is referred to The so-called “mini-shear” specimen geometry developed by Peirs et al. a, was used in this work for the quasi-static shear testing. Recent comparisons between the mini-shear and butterfly-type shear specimen geometry of Mohr and Henn . The small dimensions of the new sample required fabrication using electric discharge machining rather than CNC machining.An Instron model 1331 servo-hydraulic testing machine was used to conduct shear testing at nominal von Mises equivalent strain rates of 0.01 s−1 and 1 s−1. The as-fabricated length and thickness of each sample were measured using an optical microscope prior to testing.A Hydraulic Intermediate Strain Rate (HISR) apparatus developed at the University of Waterloo was used to perform shear tests at nominal von Mises equivalent strain rates of 10, 100, and 600 s−1. The reader is referred to Three to six repeat tests were performed for each test condition and shear stress-strain curves were determined from the measured data using the methods described in . Average stress-strain curves were generated for each test condition by: (i) interpolating a curve through the measured stress-strain data from each experiment; (ii) obtaining the stress at 0.002 strain increments from each interpolated curve; and (iii) averaging the values to obtain the average stress at each strain increment. |
where F is the measured force, t is the sheet thickness, and L is the length of the shear region (indicated in ) with nominal values of 1.92 mm for the micro-shear sample and 3.0 mm for the mini-shear geometries. The validity of the shear stress calculation for the micro-shear geometry is assessed in The strains were measured using digital image correlation (DIC) techniques. The strains (and strain rates) in this work were determined based upon local DIC strain measurements. A Point Grey Research GRAS-50S5M-C camera was employed for the quasi-static condition (0.01 s−1) and a Photron SA5 high speed camera for the higher strain rates. In the present work, the frame rates (frames per second, fps) and corresponding image sizes were: 6 fps (2448 × 2048 pixels), 1000 fps (1024 × 640 pixels), 2000 fps (896 × 488 pixels), 17,500 fps (832 × 488 pixels), and 40,000 fps (640 × 264 pixels) for von Mises equivalent strain rates of 0.01, 1, 10, 100, and 600 s−1, respectively. Full-field logarithmic (true) strain measurements were obtained using the Vic-2D software from Correlated Solutions Inc. using the incremental correlation option to account for severe local strains. Abedini et al. One aspect of the DIC measurement technique invested in this work was the choice of sampling area of interest (AOI) in determining the measured strain histories. Local strain measurements can be extracted from single points (highly variable and noisy) or averaged over a user-defined AOI (rectangular or circular, for example), which tends to smooth out noise, but introduces a length scale into the analysis. To establish a consistent methodology for the DIC analysis of the shear samples, three different AOI types were considered: a rectangular box, a circle, or 3 points from within the shear zone as illustrated in a and b for DP600 mini- and micro-shear samples, respectively. The size of the rectangular box used for the mini and micro-shear specimens was 0.3 × 1.5 mm and 0.2 × 1 mm, respectively, while 0.3 and 0.2 mm diameter circles were used for the mini and micro-shear specimens, respectively.It is important to emphasize that the reported values of strain obtained using DIC analysis are a function of the speckle pattern, resolution of the area of interest, subset size, as well as the step and filter size used in the analysis In order to quantify the effects of step size and the strain filter size in the DIC analysis, the Virtual Strain Gauge Length (VSGL) of the specimens were calculated using VSGL=Resolutionoftheareaofinterest×Stepsize×FiltersizeThe VSGL corresponds to the strain resolution of the DIC setup and is a simple parameter to study in a strain convergence analysis that accounts for the spatial resolution, step size and strain filter. It is important to note that the VSGL is not directly used within the DIC software algorithm to calculate the strains and should be interpreted as a metric to report the DIC analysis settings used in the experiments.Initially, convergence analyses were performed using a VSGL ranging between 0.2 to 0.8 mm obtained by combining different step and filter sizes. The purpose of this study was to identify an appropriate VSGL for each of the shear specimen geometries. shows the effect of VSGL on the calculated principal major strains at onset fracture (as described in ) for the mini-shear and micro-shear specimens. The measured major principal strains from DIC analysis exhibit convergence for a VSGL of 0.3 mm for both mini-shear and micro-shear specimens. Therefore, a VSGL of 0.3 mm was selected in this work to perform the rest of the DIC measurements. The adopted DIC parameters corresponding to the VSGL of 0.3 mm are shown in This section presents the measured shear stress-strain response for the two alloys at the various strain rates, as well as an examination of the conversion of the measured shear data into effective stress-strain values suitable for use in constitutive modelling. Prior to presenting the measured data, the effect of DIC sampling area of interest within the shear specimen gauge region is discussed, along with validation of the micro shear specimen geometry. Localization and failure observations are presented in Due to the small sample size and severe local strains within the gauge region it is important to characterize the effect of AOI selection used for extracting the local strain measurements. The resulting shear stress vs. maximum in-plane shear strain response under quasi-static (0.01 s−1) conditions obtained using the three sampling AOIs is shown in and exhibits good agreement until very large strains on the order of 70% for DP600. The fracture strain computed using these different methods shows some dependency upon the sampling AOI with the point measurements showing higher variation while the box and circle AOIs give similar strains. The point measurements are inherently noisy; however, the average of the three points within the shear zone provides values that are very similar to the area-averaged values. Based on these comparisons, the box AOI with the dimensions of 0.3 × 1.5 mm and 0.2 × 1 mm for mini and micro-shear specimens, respectively, were selected for the balance of the strain measurements presented in this paper.A comparison of the measured shear stress-strain response under quasi-static conditions (0.01 s−1) using the two specimen geometries is shown in for both alloys. The experimental data obtained with the mini and micro-shear specimens is in excellent agreement at quasi-static conditions with very good repeatability. For the balance of this work, the micro-shear specimen geometry was adopted for the shear experiments since the good agreement with the mini-shear experiments confirmed its suitability for the low rate experiments. Furthermore Peirs et al. The repeatability of the higher rate experiments was also examined and is shown in for the specimens tested at 600 s−1. The standard deviation in shear stress prior to peak load was approximately 6 MPa and 1 MPa for DP600 and AA5182-O sheet metal alloys, respectively. This variability is rather low and is typical of the results obtained for the other strain rates considered. Going forward the results are provided in terms of the median stress-strain curve for each rate in order to simplify the presentation.Under simple shear loading, the strain ratio, that is, the ratio of minor and major strain (ε2/ε1), is −1. To verify whether a simple shear state is maintained throughout the deformation of the mini and micro-shear samples, strain paths are obtained using the rectangular box AOI (described in ) at the center of the shear band. The measured strain paths are plotted in and compare well with the theoretical strain path, indicating that a constant simple shear strain state is maintained until failure for both the mini and micro-shear specimens. Similar strain paths with equal and opposite principal strains were also observed by Abedini et al. The effect of strain rate on the shear stress-strain response for the DP600 and AA5182-O sheet materials is shown in a and b, respectively. For DP600, the shear stress at yield and subsequent hardening response for strains up to approximately 30% are seen to increase with increasing strain rate (positive rate sensitivity). Beyond this strain level, the slope of the shear stress-strain curve decreases with increased strain rate. For shear strains above 50%, the DP600 shear specimens display negative rate sensitivity with lower stresses and earlier shear failure as strain rate increases. At low strain levels, AA5182 shows positive work hardening, but very little strain rate sensitivity. At high strain levels, the AA5182 shear specimens exhibit strongly negative rate sensitivity, with earlier localization compared to that exhibited by DP600. Note that failure strains are discussed in more detail in The drop in rate sensitivity with strain as strain rate is increased is largely attributed to the increased temperature rise with strain rate as the deformation becomes more adiabatic. At the lowest strain rate considered, 0.001 s−1, the experiment is largely viewed as isothermal since much of the heat of plastic work can be conducted away without significant temperature rise. For the highest rate of 600 s−1, the expected temperature rise can be estimated by using an adiabatic assumption and the following equation: |
where, β, the Taylor-Quinney coefficient, is the ratio of plastic work converted into heat (assumed here to be 0.9 for the highest strain rate of 600 s−1 is approximately 167°C for the DP600 and AA5182 sheet, respectively. Thermal softening characterization studies by Thompson et al. The rate sensitivity of these alloys is further explored in which plots shear stress at constant shear strain as a function of strain rate (von Mises) for both alloys. At a maximum in-plane shear strain level of 11%, the DP600 (a) exhibits strongly positive rate sensitivity. As the strain levels increase, the rate sensitivity drops at higher (100 and 600 s−1) strain rates, as reflected by the reduced slope for maximum in-plane shear strains of 60%.b) is somewhat more complex since at low temperatures and strain rates, this alloy exhibits dynamic strain aging with negative rate sensitivity due to Portevin Le Chatelier (PLC) band propagation, as reported by Rahmaan et al. b. As strain rate increases beyond 1 s−1, Rahmaan et al. A key advantage of shear experiments is the potential to acquire constitutive data at much larger effective strain levels than that normally achieved during uniaxial tensile testing which is generally limited by onset of necking instability. In the current work, conversion of experimental shear data to tensile data was performed without utilizing a yield surface assumption. Instead, an equivalent plastic work methodology was adopted. First, the plastic work was calculated from tensile experiments by Rahmaan et al. (a-b) for each alloy; the data is plotted up to conditions (plastic work) corresponding to the onset of necking in the tensile experiments ). The average shear stress ratios were found to be approximately 0.574 and 0.566 for DP600 and AA5182-O, respectively, and are relatively constant. The measured ratio of shear stress to tensile stress (σ12/σTensile) is then inserted into to obtain the equivalent stress versus equivalent plastic strain response. The shear stress ratios were assumed to be constant beyond the plastic work level corresponding to the tensile necking strain. Note that, these measured shear ratios are intermediate to the values expected were a von Mises yield criterion to be adopted (0.577) or a Hosford non-quadratic yield criterion (0.558 and 0.545 for a = 6 or 8, respectively – see ). Such non-quadratic or anisotropic yield criteria could be adopted to convert shear data to tensile data if the anisotropy coefficients were known; however, the current approach avoids the need to select a yield criterion altogether.The shear stress-strain data obtained in this work was converted to equivalent stress-strain values using the calculated shear stress ratios. It is important to mention that there is some degree of rotation of the principal directions in the shear test for DP600 and AA5182-O, respectively. The agreement between the hardening response from the uniaxial tension and shear experiments is extremely good for the DP600 sheet () for all strain rates considered (note that the highest rate differs somewhat, 1000 s−1 for the tensile and 600 s−1 for the shear experiments). Good agreement is also seen between the tensile- and shear-derived effective stress-strain response for the AA5182-O experiments (), with somewhat lower agreement at the lowest strain rate. The effective stress-effective plastic strain data derived from the shear experiments in are attractive since they are direct measures of constitutive response at large strain and offer an alternative to inverse analysis approaches to extrapolate constitutive behaviour beyond necking in tensile tests.The shear stress versus effective strain rate data in is converted to effective stress versus strain rate and plotted in . Also plotted is the uniaxial stress versus strain rate data for these alloys due to Rahmaan et al. This section examines the conditions at shear failure for the two alloys and range of strain rates considered. The observed failure modes are presented, along with detailed examination of the gradients present in the measured strains. Finally, a comparison between the strain rate sensitivity of shear fracture strain and fracture strain during tensile testing (from are images of fractured DP600 shear specimens. In general for both materials, failure occurs through exhaustion of work hardening and onset of shear instability which leads to formation of a fracture running across the gauge section.The onset of fracture is difficult to determine visually since the cracks do not open appreciably. Visual means of detecting fracture are further complicated by the painted surface required for the DIC analysis. As shown in , shear cracks are evident on the unpainted AA5182-O sample while the cracks are difficult to discern in painted samples.Unlike the uniaxial tensile test for which the onset of necking changes the strain path from uniaxial tension towards plane strain, there is no such geometric localization in shear loading for which deformation is both plane stress and plane strain until fracture without through-thickness necking. Additionally, material softening due to the nucleation and growth of voids is limited in shear as there is no hydrostatic stress to promote void growth. Consequently, the onset of shear localization into narrow adiabatic shear bands or the onset of shear cracking can be detected when the hardening capacity is exhausted according to the Zener and Hollomon show the shear stress-strain response and hardening rate for the DP600 and AA5182-O samples, respectively. A sudden decrease in the hardening rate is observed at peak load which continues until complete failure. Moreover inspection of the local effective strain rate in (c and d) and 19(c and d) also shows an increase in the local strain rate from peak load to complete failure. This behavior indicates onset of localized deformation of the shear band resulting in final fracture.Detecting fracture strain based on visual observation of DIC images introduces challenges associated with inconsistency in detecting cracks due to variation in the speckle pattern, the presence of the paint layers, and absence of tensile opening of the crack. On the other hand, considering the strain at onset of location () as the fracture strain may be conservative measure, but is repeatable and eliminates the need to detect fracture based on visible cracking. The strain at which visible cracking was observed in the DIC images is indicated in (open circles) and does occur shortly after the localization criterion is met. Thus, the strain at onset of localization has been adopted herein to characterize the fracture strain. The fracture strains of DP600 and AA5182-O were obtained for the range of strain rates from the measured experimental data. The effect of strain rate on the localization (fracture) strains for DP600 and AA5182-O sheet is shown in a and b, respectively. For an increase in strain rate from 0.01 to 600 s−1, the von Mises equivalent strain at fracture decreased from 90% to 68% (22% decrease) for DP600 and from 96% to 64% (32% decrease) for AA5182-O. A similar decrease in failure strain with increased strain rate was also reported by Roth and Mohr In order to examine the evolution of strain once localization initiates within a specimen, the equivalent strain from equally spaced points along a horizontal line-slice of length 2 mm (as shown in a shows a plot of the maximum in-plane shear strain versus position along the line slice at strain rates ranging from 0.01 to 600 s−1 for DP600 (a) and AA5182-O (b). All of the measured strain distributions show an increase in strain towards the centre of the shear zone. There is also a significant decrease in the strain measured using the DIC system at onset of localization as strain rate increases, as reflected by the lower peak strains with increased strain rate.The evolution of the strain distribution measured using the DIC system after the onset of localization is plotted in for a strain rate of 0.01 and 600 s−1. Once localization initiates, deformation becomes more focused within a narrow band at the center of the shear zone while away from the localized band, strain remains constant.To further investigate localization of the shear band for DP600, measurements of shear strain were performed at the microstructural level based upon local grain rotation. Fractured DP600 specimens tested at 0.01 s−1 and 100 s−1 were mounted and polished to a diamond grit size of 0.25 µm. The polished surface was etched with 2% Nital to reveal grain boundaries under the optical microscope as indicated in , which correspond to specimens tested at 0.01 s−1 and 100 s−1 von Mises equivalent strain rates, respectively. Only DP600 was considered for this study due to the strong contrast between the ferrite and martensite phases which enables measurement of grain orientation . During the shearing operation, grains have tendency to rotate within with the shear band. An angle of rotation can be calculated by assuming grains were initially aligned parallel to the rolling direction and any change in the orientation of a grain is defined as shear angle, α (as shown in ). The magnified views (a1 and a2) indicate the shear angle near the fractured edge which corresponds to the center of the shear band, while the magnified views (b1 and b2) correspond to the region in the shear band, but away from center. Away from the shear band, the material is undeformed and therefore grains are oriented randomly as shown in the magnified views (c1 and c2). A sharp increase in shear angle is observed near the center of the band (micrographs a1 and a2) due to the deformation being localized to a smaller band. The material outside the localized band (micrographs b1 and b2) does not undergo further deformation after the onset of localization and therefore has a lower angle of rotation or strain, also seen in The shear angle represents the amount of deformation under shear loading and can be converted to an equivalent strain using . The shear angle was measured by drawing lines of approximately 20 μm length along the rotated grains using software from Image-Pro and the angle between the line and horizontal direction was defined as the shear angle, α (where α=tan−1γ). The tilt angle of shear band was converted to an equivalent strain using for roughly 100 locations across the shear band of the fractured DP600 specimens tested at von Mises equivalent strain rates of 0.01 and 100 s−1. shows the strain distributions across the shear band calculated using the grain rotation technique and the distribution extracted from the DIC image near failure. The two techniques are in close agreement with each other away from the centre of the shear zone. However, near the center of localized band, the grain rotation technique reveals much sharper strain localization and higher peak strains than seen in the results from the DIC analysis.One reason for the higher strains measured using the grain rotation technique versus the DIC measurements is the inherent resolution used for each method. For the DIC analysis, the imaging is performed using an effective gauge length (VSGL) of 0.3 mm whereas the optical microscopy offered a resolution of 0.5 µm/pixel for the grain rotation technique. Thus the severe strain localization cannot be captured by the DIC method. This behavior may be similar in AA5182 since indicates similar localization of deformation across shear bands in DP600 and AA5182.Comparison of the strain distributions obtained using the grain rotation technique in a and b, reveals that local strain at final fracture actually increases with an increase in strain-rate. This trend (shown in from the DIC measurements (also shown in ) which indicates that the strain at the onset of localization and the DIC-measured failure strain both decrease with increased strain rate. Essentially, the effect of the temperature rise with increased strain rate is to trigger an earlier instability and, for the highest rates, onset of adiabatic shear localization. This localization results in higher local strains at fracture. The peak strain resolved by the DIC measurement, however, is lower due to the imposed gauge length (VSGL) and optical resolution. Similar localization behavior was reported by Haltom et al. Here, the measured failure strains from the current shear experiments are compared to failure strains from the tensile samples tested by Rahmaan et al. . As part of this work, the reduction in area from the tensile samples of Rahmaan et al. |
in which Ao is the area of the specimen prior to testing and Af is the final area of the specimen measured using optical microscopy after failure. The resulting failure strains from the tensile and shear experiments are shown in as a function of von Mises equivalent strain rate. Also plotted are the maximum in-plane shear failure strains for reference.DP600 exhibits an overall trend towards increased failure strain under tensile loading with an increase in strain rate, as shown in a. For an increase in strain rate from 0.001 to 1000 s−1, the tensile failure strain increased by 22%. In contrast, the maximum in-plane shear failure strain for the range of strain rates considered in the shear experiments (0.01 to 600 s−1) decreased by 17%. For the same strain rate increases, the AA5182-O sheet exhibited a 56% increase in tensile failure strain and a 22% decrease in maximum in-plane shear failure strain (b). The improvement in tensile failure strain with strain rate for both alloys is attributed to their positive rate sensitivity, which acts to delay onset of necking and potentially retard damage development under higher temperatures b. Above 1 s−1, dynamic strain aging is suppressed The current DIC measurements of failure strain have demonstrated a complex interaction between adiabatic heating and strain rate hardening that resulted in increases in failure strain under tensile loading as strain rate is increased, but a corresponding decrease in failure strain under shear loading. Such complex sensitivity to loading rate can have important implications for CAE prediction of failure. It is very common practice for CAE predictions of fracture to utilize quasi-static rather than dynamic characterization of failure strain as a function of stress triaxiality The microstructural measurements of strain localization for DP600 show that local shear strains at failure can increase with strain rate, in direct contrast to the DIC measurements. This outcome is a consequence of the adiabatic shear bands localizing to a width much less than the gauge length of the DIC measurements. Therefore care will be required to consider length scales and mesh effects when modelling shear failure at high rates of deformation.On-going work will focus on characterization of the thermal conditions occurring during high rate loading in shear and in tension with in situ high speed thermal imaging. Coupled thermo-mechanical modelling will be required for intermediate strain rates cases for which neither an isothermal nor an adiabatic assumption is appropriate It is expected that accounting for temperature rise due to plastic work will become even more significant when one considers the trend towards adopting higher strength materials for vehicle lightweighting, such as hot stamped boron steels The experimental constitutive characterization presented in this paper using simple shear loading can be useful to extend material work hardening curves beyond that achieved under uniaxial tension which is limited by onset of necking. The determination of the shear stress ratio relative to the tensile stress along specific material directions for equivalent levels of plastic work can also be used in calibration of yield functions for anisotropic materials.The “micro-shear” scaled version of the “mini-shear” specimen originally developed by Peirs et al. An experimental methodology was established to obtain the hardening behaviour to large strain levels by using a tensile and shear test and the DIC strain measurements that can be adopted for elevated strain rates as well as anisotropic materials.At strains below uniform elongation, the shear stress measured for DP600 exhibited positive strain rate sensitivity, whereas low rate sensitivity was observed for AA5182-O. At shear high strains, both alloys exhibited negative strain rate sensitivity due to thermal softening.The shear strains corresponding to the onset of shear localization, as determined using the Zener-Holloman criterion for shear localization, were close to (preceded) the occurrence of observable cracks. For an increase in strain rate from 0.01 s−1 to 600 s−1, the maximum in-plane shear strain to failure (onset of localization) decreased by approximately 19% and 28% for DP600 and AA5182-O sheet metals, respectively.The ability of DIC methods to measure local shear strains to failure at high rate was evaluated, and compared with measurements of the microstructure using grain rotation technique. The microscopic measurements revealed much sharper strain localization and higher peak strains at fracture near the center of localized band as opposed to the DIC measurements.Effect of steel wrapping jackets on the bond strength of concrete and the lateral performance of circular RC columns► Bond stress–slip behavior of concrete confined by steel wrapping jackets is provided. ► The steel wrapping jackets increase the ductile behavior of lap-spliced RC columns. ► The bond strength at lap splicing region with the steel wrapping jackets increases.In this study, the bond behavior between steel reinforcing bars and concrete confined via steel wrapping jackets is estimated. Lateral bending tests are conducted for the reinforced concrete columns with continuous longitudinal reinforcement or lap-spliced longitudinal bars confined by the steel wrapping jackets. It is found that the jackets increase the bond strength and ductile behavior due to the transfer of splitting bonding failure to pull-out bonding failure. In the column tests, the steel wrapping jackets increase the flexural strength and ultimate drift for the lap-spliced column. However, the jacket for the column with continuous longitudinal reinforcement only increases the ultimate drift since the flexural strength depends on the yield of reinforcement. Finally, this study suggests a basic concept for determination of the thickness of the steel wrapping jackets which is different from the conventional method.thickness of the concrete cover for the longitudinal steel barspeak compressive strength of the unconfined concreteconfining pressure provided by the transverse steel reinforcement at the strain level of 0.1%, fje |
= 1.1fyjperimeter in the column cross section along the lap-spliced bar locationsvolumetric ratio of longitudinal reinforcing barWith the prevalence of social media and the Internet since the late 1990s, the knowledge of major seismic events in more heavily populated areas, such as Chirstchurch in New Zealand and Tohoku in Japan, has increased and thus, the public perception of “safe” structures is becoming more important. Therefore, it is sensible to emphasize seismic protection for civil structures with a particular goal of placating public perception of the safety of the civil structures. Most countries in area of high or moderate seismic risk have seismic codes that reflect their seismic situations and design philosophies. However, bridges that have been in service for long periods of time may not have sufficient seismic protection due to their non-seismic design and construction. Bridge failures during previous earthquakes have been primarily caused by inadequate construction details such as inadequate lateral reinforcement or insufficient lap length of the bars For retrofit of RC beam–column joints, Karayannis et al. The bond between the steel reinforcing bars and concrete is a crucial factor for RC columns exposed to seismic events. In particular, RC columns with lap-spliced reinforcements in the plastic region demonstrated a splitting bond failure and did not provide adequate ductility The first aim of this study is to demonstrate that steel wrapping jackets increase the bond strength of concrete. While steel wrapping jackets have been applied previously to confine lap-spliced RC columns, the results were not satisfactory In this study, the specimens of concrete cylinders prepared were expected to induce splitting bond failure in an unconfined state; concrete cylinders with dimensions of 100 mm × 200 mm were used. Stainless steel jackets with the dimensions of 324 mm × 200 mm were prepared in order to confine the concrete cylinders; the width was 10 mm larger than the perimeter of the cylinder in order to create the welding overlap. Steel jacket thicknesses of 1.0 mm and 1.5 mm were chosen to assess how the amount of confinement has an effect on the bond behavior. There were three types of specimens for the splitting failure mode: (1) unconfined, (2) confined by a 1 mm jacket, and (3) confined by a 1.5 mm jacket. Each type had two specimens, and a total of six specimens were prepared for the bonding tests.The yield strength of the steel jackets was measured to be 288 MPa, and the measured peak strength of the concrete was 30 MPa. The total length of the reinforcing bars was 260 mm, and a part measuring 60 mm protruded beyond the top surface of the specimens. The embedment length of the bars was 150 mm, with 25 mm of length at the top and bottom of the specimens wrapped with oil paper. The D22 reinforcing bar (with a nominal diameter of 22.2 mm) was used in the tests. The detail description of the jacketing process can be found in Choi et al. shows the jacketing process briefly. First, a rolled steel jacket was prepared and the concrete surface was treated. Then, two clamps and three steel bands were used to press the steel jacket onto the concrete surface. Next, the steel jacket under an external pressure was welded and attached tightly to the concrete surface after the subsequent removal of the clamps and the steel bands.The bond test in this study was a push-out test, and illustrates the test setup graphically. A specimen was placed on a support frame that has a circular rigid plate at the top with a hole of 25 mm at the center of the plate. The protruding reinforcing bar was pushed down through the hole by an actuator, and the slip was measured by a displacement transducer fixed using a magnetic base on the bottom plate of the support frame. The measured slip of the reinforcing bar was used to calculate the bond stress. During the push-out process, the compression plate in b was just contacted on the top of the extrusion bar and thus, the connection was similar to a pin and any bending loading was not transferred to the bar. All specimens were pushed out up to 22 mm, which is the distance from the start of one rib to the end of an adjacent rib of the reinforcement.The failure mode of the unconfined specimens was the splitting mode as initially planned. indicate the inside and outside views of the unconfined and confined specimens after the completion of the test, respectively. For the splitting failure mode, radial cracks developed due to the splitting stress, and the concrete surface contacting the reinforcing bar was clear because the bar slipped on the surface. For the pull-out failure mode, the radial crack was not visible to the naked eye. The concrete between the ribs of the reinforcing bar was sheared off, and the smoothened contact surface was attributed to the friction between the two concrete surfaces.Assuming that the bond stress (τb) of a reinforcing bar embedded in the concrete is distributed uniformly over the development length (Lb), the applied force (F) in the bar can be calculated from the equilibrium of forces as follows:where db is the nominal bar diameter of 22.2 mm and the uniform bond stress for each specimen was calculated using Eq. . The experimental bond stress–slip curves were compared with the nonlinear expression provided by Ciampi et al. , (2) the plateau state, (3) the linear softening phase, and (4) the residual stable plateau. Each state is described below:The pull-out bond failure: smax |
= 1 mm, s2 |
= 3 mm, sf |
= clear rib spacingThe splitting bond failure: smax |
= |
s2 |
= 0.6 mm, sf |
= 1 mmwhere τb,max and τb,f represent the maximum bond strength and the frictional bond strength value, respectively. Also, the smax is the slip limit for the maximum bond stress, s2 is the limit for the stable bond stress range, and sf is the slip starting frictional slippage. shows the bonding strengths of the unconfined and confined specimens. In addition, shows the bond stress–slip relationship and the comparison between the experimental results and analytical model. The results of the unconfined and confined specimens are compared in a, the experimental results for the splitting failure mode correspond well to the analytical model. However, in the case of the pull-out failure mode for the confined specimens in b and c, the experimental curves did not show a plateau phase following an increasing branch as the model does, although the other sections matched with the model well. The bond stress–slip curves in previous studies did not demonstrate the plateau for the pull-out failure mode clearly Four circular columns, each 400 mm in diameter and 1400 mm in height, were fabricated with a ratio of 3.5, as indicated in . Each column was fabricated with 16-D13 longitudinal bars and D10 bars with a spacing of 160 mm for the transverse reinforcement. The concrete cover of the specimens was 40 mm. The measured yield strength of the longitudinal reinforcements was 325 MPa, and the measured compressive strength of the concrete was 20 MPa.Two of the four columns had a 50% lap splice in the longitudinal reinforcements from the starter bars projecting from the foundation. These specimens are indicated as SP50-NSJ and SP50-SJ1 in . In this paper, NSJ refers to the non-steel jacket and SJ1 represents the specimen with steel jackets. A 50% lap splice indicates that half of the 16 bars were spliced from the starter bars, and the length of a lap splice was 200 mm. The remaining columns were constructed with continuous longitudinal reinforcements and are indicated as SP00-NSJ and SP00-SJ1. One sample of each type of specimen was jacketed at the bottom of the column using the steel wrapping jacketing method. The steel jacket used to retrofit the bridge columns provides a lateral confining pressure on the concrete and can be considered as a continuous hoop reinforcement. The required thickness of the steel jacket (tj) based on the equivalent volumetric ratio of the hoop reinforcement is generally calculated using the following three design equationstj=D40.16fc′fje(0.5+1.25Pfc′Ag)+0.13(ρl-0.01) where D is the column diameter; fje |
= 1.1fyj in which fyj is the yield strength of the steel plate; fc′ is the peak compressive strength of the unconfined concrete; Ag is the gross area of the column cross-section; and ρl is the volumetric ratio of longitudinal reinforcing bar.The measured yield strength of the steel plate was 288 MPa. Using Eqs. , the estimated thicknesses of the steel jackets were 0.715 mm, 0.833 mm, and 0.521 mm for ACT-32, AASHTO, and Caltrans, respectively. The maximum thickness was 0.833 mm; therefore, this study used the 1.0 mm thickness for the steel plate conservatively. The length of the steel jackets (lj) was determined to be 400 mm using the following equation where D and L are the diameter and the length of the column, respectively.The jacketing procedure for the columns was mechanically the same as that for the bonding test. However, clamps could not be used for the column; thus, the combination of a cable and a special device was used to press the steel jacket as shown in . The special device pulled the cable out by rolling a nut. A total of four cables were placed on the steel jacket, and the tension of the cable was estimated to be approximately 8.8 kN.The test setup was established for a combination of axial and lateral loadings using the column footing assemblages, as shown in . A constant axial load of 0.1fc′Ag was applied by introducing the prestressing force of two strands against the reinforced strong floor via a loading frame. Cyclic lateral loads were applied using a hydraulic actuator at a height of 1400 mm. All columns were instrumented to measure the lateral displacements and corresponding applied loads. The loads were measured using the calibrated load cell of the actuator. A displacement transducer was installed on the reference frame at a height of 1400 mm from the bottom of the footing. A quasi-static load was applied at the top of the columns under displacement control. A lateral load was applied in the form of a drift ratio starting from ±0.25%, which was first increased to ±0.5% and was then increased in 0.5% increments up to failure. Two cycles were applied for each drift ratio, which was the ratio of the input displacement to the column height of 1400 mm.The cyclic behavior of the force–lateral displacement is shown in ; the displacement was measured at the loading point using the actuator stroke. The corresponding envelope curves are illustrated in presents the summary of the test results, such as the flexural strength, yield and ultimate drift ratios, and displacement ductility. The ultimate point was estimated to be 85% of the peak shear force in the degrading zone. The yield point was the intersection point of the horizontal line that indicates 85% of the peak force and the line from the origin to the point of 75% of the peak force. This study compared the average values of the pushing and pulling results. For the continuous reinforcement column SP00-NSJ, the yield and ultimate points occurred at a drift of 0.694% and 4.394%, respectively; the displacement ductility was 6.129. For the jacketed continuous reinforcement column SP00-SJ1, the yield and ultimate points were observed at 0.772% and 6.982%, respectively; thus, the displacement ductility was 9.059. The steel wrapping jacket increased the ultimate drift by 59.0% compared with that of the unjacketed specimen although the flexural strength of the jacketed specimen showed nearly the same strength as the unjacketed specimen. The flexural strengths for the two specimens were 97.1 and 94.6 kN, and the difference was only 2.6%. Accordingly, the steel jacket increased the ductile behavior of the continuous reinforcement specimen, but it had no effect on the flexural strength. Also, the steel jacket delayed the yield point by 11.2%.For the lap-spliced specimen SP50-NSJ, the yield occurred at 0.618% drift ratio, which was 12.3% less than that for the SP00-NSJ specimen. Also, the drift ratio was 1.975% for the ultimate state; thus, the displacement ductility was 3.193, which was almost half of the ductility of the SP00-NSJ. When a steel jacket was applied to the lap-spliced column (SP50-SJ1), the yield and ultimate points developed at 0.665% and 5.598% drift ratios, respectively, and the displacement ductility was 8.40. Thus, the steel jacket increased the ultimate drift 2.83 times. Also, the jacket increased the flexural strength by 19.4% from 79.7 kN to 95.2 kN. The strength of the jacketed lap-spliced specimen was almost identical to that of the continuous reinforcement specimens. The lap-spliced specimen was observed that the steel jacket increased the ultimate drift and flexural strength.The initial stiffnesses of the force-deformation curves in . The jacketed specimen with the continuous reinforcements demonstrated less stiffness; however, the jacketed lap-spliced specimen demonstrated more stiffness. Therefore, it appears that the jacket did not influence the initial flexural stiffness of the columns; the steel wrapping jacket did not behave compositely with the concrete and did not influence the flexural stiffness. This non-composite behavior is beneficial in the seismic retrofitting of RC columns because it does not alter the original stiffness of the columns. The conventional steel jacketing method produces composite behaviors between the jacket and the concrete as a result of the bond of the grout so that it increases the stiffness and shortens the fundamental natural periods of the retrofitted structures. The increased stiffness may draw more seismic acceleration into the columns; thus, the effectiveness of the steel jackets could be reduced. shows the failure mode of each specimen. The continuous reinforcement specimen SP00-NSJ demonstrated a typical buckling failure of reinforcement. The reinforcing bars located furthest from the neutral axis were buckled and subsequently fractured. The specimen demonstrated yielding behavior because of the yield of reinforcement, and the cover concrete was spalled off. The reinforcement was not protected from the buckling as a result of the spalling of concrete cover, and the flexural strength was degraded in relation to the buckling of the reinforcement. For the jacketed continuous reinforcement specimen SP00-SJ1, the buckling of the reinforcing bars was delayed since the cracked cover concrete was confined by the jacket, which postponed the reinforcing bars from the buckling. Accordingly, the flexural strength of the specimen was maintained after the yield until the drift ratio of 6.44% was reached. The abrupt degradation of the flexural strength in b was caused by the tensile fracturing of the reinforcing bars. The reinforcing bars in For the lap-spliced specimen SP50-NSJ, the flexural strength was 21.8% lower than that of specimen SP00-NSJ because the lap-spliced reinforcements failed due to slippage before yielding. After the failure, the flexural strength degraded sharply. The continuous reinforcements in the specimen were buckled and lost strength continuously. When the lap-spliced specimen was confined using the steel wrapping jacket, the bond strength increased and caused the lap-spliced reinforcements to yield, which increased the flexural strength to the same level as that of the continuous reinforcement specimen. Also, the jacket constrained the cracked cover concrete and delayed the buckling of the reinforcement as in the case of specimen SP00-SJ1.Strain gauges were mounted on the surfaces of the starter bars and longitudinal bars of the as-built and jacketed columns at the plastic zones. The stresses in the bars at the measuring locations can be estimated using the measured strains and elastic-perfectly plastic behavior of steel. Using the equilibrium condition, the average bond stress (τb) along the surface of the starter bar can be calculated from the estimated stress of the bar as follows:where fs is the stress at the bar; dlb is the diameter of a longitudinal bar; and Ls is the length of the lap splice. a compares the developed stresses in the starter bars of the lap-spliced columns with the stresses in the longitudinal bars of the continuous reinforcement columns as a function of the drift ratio. When the lap-spliced column was retrofitted by the steel wrapping jacket, the developed stress in the starter bar reached the yield stress of steel (400 MPa), and it was 51% larger than the peak stress in the starter bar of the unjacketed column. Also, the starter bar demonstrated a similar trend for the stress in those of the longitudinal bars in the continuous reinforcement columns. b compares the stresses in the starter or the longitudinal bars of the lap-spliced columns, and the developed stress in the longitudinal bars was close to that in the starter bars. The peak bond stress of the jacketed column SP50-SJ1 was 6.5 MPa, which appeared with a yield stress of steel and was 51% larger than the peak bond stress 4.29 MPa in the unjacketed column SP50-NSJ. For the unjacketed column, the bond stress was suddenly degraded at a drift ratio of 1.78%, which corresponds to that for the peak flexural strength in c. For the jacketed column, the peak bond stress was developed at a drift ratio of 2.08% and was maintained at the peak value. This coincided with the behavior of the envelope curve for the column; the envelope reached the peak flexural strength at a 1.91% drift ratio and was maintained until a 3.18% drift ratio. Thus, it was found that the peak bond stress was developed at the peak flexural strength and retained until the degradation of the flexural strength.For the continuous reinforcement columns, the steel wrapping jacket did not increase the stresses in the longitudinal bars. However, the jacket maintained the peak flexural strength up to 8.27% drift ratio without degradation, which was 2.16 times as large as the unjacketed continuous reinforcement column SP00-NSJ in . The more ductile behavior of the jacketed continuous reinforcement column SP00-SJ1 was resulted from the jacket delaying the buckling of the longitudinal reinforcing bars, and the delayed degradation of the flexural strength of the SP00-SJ1 was not related to the bond stress.The primary roles of the steel wrapping jacket are to increase bond strength and delay the buckling of the longitudinal bars because it provides confining pressure for the lap-spliced RC columns. Therefore, the jackets increased the flexural strength and ultimate drift. For a continuous reinforcement column, the jacket did not contribute to the increase in the flexural strength because the flexural strength depended on the slip and yield of reinforcing bars. Based on the above findings, the thickness of the steel wrapping jacket should be determined from the bonding and confining actions. However, Eqs. , which are used to determine the thickness of the steel jacket, were based on the failure of steel during an axial compressive test as indicated by Priestly et al. where fh represents the confining pressure provided by the transverse steel reinforcement at the strain level of 0.1%, D is the diameter of the column, and Ej is the elastic modulus of the jacket. Seible et al. where p is the perimeter in the column cross section along the lap-spliced bar locations, n is the number of spliced bars along p, Abl is the area of one main column reinforcing bar, fyl and dlb are the yield strength and diameter of longitudinal bars, respectively, Ls is the length of the lap splice, and c is the thickness of the concrete cover for the longitudinal steel bars. The elastic modulus of steel is 200 GPa, and the yield strength of the steel reinforcement is 400 MPa. Thus, the fh and fl for the column in this study are equal to 0.578 and 1.554 MPa, respectively. If only the slippage is considered, the required thickness of the steel jacket was 0.976 mm. However, the jacket thickness required to restrain the buckling of the longitudinal reinforcement up to a demand-ductility has not yet been discussed clearly. Therefore, further study is required in order to set up a design procedure for steel jackets based on the slippage at the lap-spliced zone and the buckling of the longitudinal reinforcement.The steel wrapping jacket was installed using the same mechanism of the prefabricated FRP sheet jacket The total thickness of the wrapping steel jacket will increase for an unretrofitted column with large diameter. In the case, the weight of the jacket and pressing method could be potential problems. However, to satisfy the required thickness of the jacket, a multi-layered jacket consisting of several thin plates can be provided. In addition, each layer can be comprised of two or three pieces which can be welded together in site. Thus, the proposed jacketing method of wrapping steel plates can overcome potential problems encountered during construction.This study conducted bond strength tests of concrete confined by steel wrapping jackets, as well as, bending tests for RC columns jacketed by the steel wrapping jackets. This study found that the steel wrapping jacket transferred the splitting bond failure to the pull-out bond failure and increased the bond strength of the concrete. Also, it appears that the steel jacket thickness had a limited ability to increase bond strength because the jackets of 1.0 and 1.5 mm demonstrated almost identical bond strength.The jacket in the bending tests of the continuous reinforcing RC columns contributed to increase the ultimate drift and displacement ductility because it prevented the cracked concrete cover from spalling off and thereby delaying the longitudinal reinforcing bars from the buckling. For the lap-spliced RC column, the jacket further increased the flexural strength because the reinforcement yielded before starting the slip at the lap splice zone due to the jacket’s contribution to increasing bond strength. This study estimated the developed bond stresses at the lap-spliced zones. The bond strength of the lap-spliced bar in the jacketed column was estimated as 6.5 MPa that was 1.52 times as large as that of the lap-spliced bar in the unjacketed column. The flexural strength of the jacketed lap-spliced column was 1.32 times as large as that of the unjacketed column. Consequently, it was reasoned that the increment of the flexural strength of the lap-spliced column was due to the increment of the bond stress in the lap-spliced bars providing lateral confining pressure of the steel jacket.The critical factors of failure for the lap-spliced and continuous reinforcement RC columns were the slip in the lap-spliced zone and buckling of the reinforcing bars. Steel wrapping jackets acted on these factors to improve the seismic performance of the RC columns. Accordingly, the thickness of the steel jacket should be determined based not on the failure of steel in the compressive test of the concrete, but on the bonding and confining actions.A time-efficient method for predicting ratchetting strain is proposed. The ratchetting strain at any cycle is determined by finding the ratchetting rate at only a few cycles. This determination is done by first defining the trajectory of the origin of stress in the deviatoric stress space and then incorporating this moving origin into a cyclic plasticity model. It is shown that at the beginning of the loading, the starting point of this trajectory coincides with the initial stress origin and approaches the mean stress, displaying a power-law relationship with the number of loading cycles. The method of obtaining this trajectory from a standard uniaxial asymmetric cyclic loading is presented. Ratchetting rates are calculated with the help of this trajectory and through the use of a constitutive cyclic plasticity model which incorporates deviatoric stresses and back stresses that are measured with respect to this moving frame. The proposed model is used to predict the ratchetting strain of two types of steels under single- and multi-step loadings. Results obtained agree well with the available experimental measurements.components of deviatoric stress tensor incrementcomponents of back stress tensor incrementcomponents of mean-stress tensor in deviatoric spaceCyclic ratchetting, which occurs under asymmetric cyclic stress, refers to progressive accumulation of plastic strain as the number of cycles increases. The ratchetting deformation accumulates incrementally with the applied number of cycles, and it may not cease until fracture. The ratchetting contributes to the material damage, and thus results in reduced fatigue life Ratchetting has been observed in many engineering components. Welded nozzles of pressure vessels, pipelines, and micro-electromechanical systems are among these components. Cyclic ratchetting of rolling stock due to high compressive stresses that are superimposed on cyclic shear produced by friction at the wheel/rail contact is another example. In such cases the long-term effect of ratchetting is of interest.The ratchetting behaviour of different materials has been studied experimentally, and different material models capable of predicting ratchetting have been used widely in recent years. However, less attention has been devoted to ratchetting at higher numbers of cycles The first general cyclic plasticity model, proposed by Mroz Ratchetting calculations using available models are very time consuming. Moreover, the low ratchetting rate at higher cycles requires using a higher number of increments and, hence, a long calculation. Because the ratchetting rate is small and subject to transient changes, it is imperative to study ratchetting over many cycles. Methods with low complexity and fast response for both low (few hundred) and high (few thousand) cycles are of considerable interest.The focus of the current study is on predicting long-term ratchetting strain. It is shown that as the ratchetting progresses, a trajectory for the origin of stress may be defined in deviatoric stress space. The starting point of this trajectory coincides with the origin of the initial stress at the beginning, and approaches the mean stress as the loading progresses. The method for obtaining this trajectory from a standard uniaxial asymmetrical cyclic loading is presented. Using this knowledge, applied to a constitutive cyclic plasticity model which incorporates deviatoric stresses and back stresses that are measured with respect to this moving origin, ratchetting rates for different cyclic loadings are calculated in a time-efficient manner.First, the concept of moving stress origin is introduced. Then, the constitutive cyclic plasticity model which is based on this concept is established, and the method for evaluating the material constant is presented. Several examples, including single step and multiple step ratchetting problems, are solved and compared with available experimental results. Results obtained agree with the available experimental measurements. To show the merits of the proposed model, a comparison is made between the method presented here and other ratchetting models.A close examination of ratchetting behaviour suggests that the stress and back stress employed in constitutive equations can better characterize ratchetting if they are measured with respect to a moving frame of reference. With the aid of several schematic representations, shows an uniaxial asymmetric loading (a loading where maximum and minimum values of stress are not equal) having stress amplitude σa and mean stress σm and shows the relation between the mean stress value and the initial ratchetting rate (schematically the strain ratcheting rate in the first cycle). The figure reveals that loadings with different mean stresses have different ratchetting rates: the larger the mean stress, the higher the ratchetting rate, findings that are depicted in several graphs in . By introducing a moving position, Mxx, for the stress origin the decrease in ratchetting strain as the number of cycle increases can be related to the reduction of mean stress if measured relative to Mxx. The relationship between this relative mean stress and ratchetting rate is shown in Taking into account the real behaviour of the material, the position of the stress origin trajectory can be determined in each cycle by relating its ratchetting rate to the corresponding relative mean stress that would yield the same initial ratchetting rate, a finding portrayed schematically in It will be shown subsequently that the stress origin trajectory obeys a power law relation with respect to cycles. The change in stress origin is considered in the cyclic plasticity model employed here.Within the context of time-independent material behaviour, the von Mises yield criterion is considered as where σy is the yield stress. The shape and size of the yield surface is assumed unchanged during plastic loading. The plastic flow rule is assumed to be in the normal direction to the yield surfaceThe consistency condition requires that the stress state lies on the yield surface during plastic loading, which mathematically iswhere daij and dSij are the tensors of back stress and stress increment in deviatoric space.where C′ and γ are material constants. In order to incorporate an uncoupled format of this model, dividing the right-hand side of Eq. by the corresponding plastic modulus the model, and rearranging the terms yieldsdaij=Ep(23(C′/γ)nij-aij)(23(C′/γ)-aijnij)dp,Using a Ramberg–Osgood equation for representation of the plastic modulus Based on above equations, Ep will be defined asηmax is the value of η at the initiation of the plastic loading η=32(σLσy(Sij-aij)-Sij)(σLσy(Sij-aij)-Sij).Given the moving reference, we may now place the described hardening rule in relative form by replacing Sij and aij by relative values measured with respect to this reference.The proposed method requires two sets of material constants: uniaxial cyclic stress–strain curve constants (K′, |
n), and ratchetting curve constants K″ and n″, defined as follows. The first two constants can be obtained from symmetric uniaxial loading. It is important to note that the cyclic stress–strain curve has a significant effect on the ratchetting strain calculations, so an appropriate representation of the cyclic stress–strain curve is a prerequisite of any ratcheting model compares the introduced model's prediction and the experimental stabilized stress–strain hysteresis loop of strain-controlled uniaxial loading with strain amplitude of εa=1% for St 1070 Ratcheting constants are obtained from an asymmetric stress controlled test by directly relating the stress to the position of the stress trajectory through the following relation:where N is the number of cycles and is directly related to the position of the stress reference Mxx and mean stress σm bywhere SxxM=23σm represents the deviatoric component of the axial mean stress. shows a schematic representation of the procedure needed for defining the ratchetting curve δ vs. N. In , δ-ε˙ is constructed based on the constitutive relations discussed above. The experimental results of an uniaxial asymmetric loading yield the loading shown in for every δ (0<δ<1) corresponding number of cycles. A graph is then constructed for δ vs. N by repeating this procedure for different values of δ, as shown in is useful for uniaxial and single-step (constant mean stress) cyclic loading. A generalization is needed for using this method in any multiaxial and multi-step (changing mean stress) loadings.Noting that Mxx possess an exponential trend, starting at zero (for a virgin material) and ending at mean stress, we can use the following variational form to represent the Mij tensor suitable for multiaxial stress loading:where ΔMij is the variation of the stress origin Mij within ΔN cycles, and c is a curve-fitting parameter. Also, SijM is the mean stress tensor defined in deviatoric stress space. Availing of the Chaboche model . To illustrate how this model describes Mij, let Mij consist of L different parts defined byFurther, let the variation of each part take the following form:where Δ(Mij(z)) is the change of the zth part of Mij in ΔN cycles, and Mij(z)f=rzSijM0<rz<1 withConstants cz and rz are determined by using existing methods (Jiang rK=((Mxx(K)-Mxx(K-1))/(NK-NK-1))-((Mxx(K-1)-Mxx(K-2))/(NK-1-NK-2))cKSxxM,where Mxx(K) is the stress origin value in an asymmetric uniaxial test at cycle NK. This concept is shown in . Also, SxxM=23σM represents the deviatoric component of the axial mean stress.The number of segments “L” has minimal effect on computational time. Therefore, it is possible to use a larger number of segments for better curve fitting. The main advantage of using more than one term for Mij is its ability to simulate ratchetting rate for multi-step cyclic loading. provides a flow chart describing the method of calculating the ratchetting strain.Two uniaxial asymmetric cyclic loadings, one with a positive mean stress and the other with negative mean stress, are considered first. In the first example, with σm=+380 MPa, the predicted ratchetting direction is positive. In the second example, with σm=−205 MPa, the predicted ratcheting rate is in the negative direction, which is in agreement with experimental results. In , the ratchetting rates with respect to cycles are compared with the experimental values In this section four multiaxial loadings are considered, and the results are compared with experimental results of Chen et al. . These loading paths were conducted at room temperature under load control for axial loading and under strain control for torsional loading.Only 12 cycles are used to calculate the ratcheting rates, at maximum, in each 1000 cycles. The prediction results agree well with experimental data. shows predictions of the cyclic shear stress–strain response and the axial-shear stress response under non-proportional loading of case 3, while shows the axial-shear stress response for case 4.Two uniaxial and multiaxial two-step loadings are considered here. In the first example, data for multiaxial loading have been compared with available experimental data , the experimental results show that the ratchetting rate is reversed when the second load step starts. present comparisons between predicted ratchetting strains by the proposed method and experimental results. The proposed method predicts the axial ratchetting direction very well; however, the method over-predicts the ratchetting rate in the shear direction for the first step. No shear ratcheting rate is predicted in the second load step, a result in agreement with experimental results. It is worth noting that for experimental results, although proportional loading is applied in the second load step, the material shows non-proportional behaviour in this load step. This finding agrees with the proposed movement of the stress origin. the rate of ratchetting is reversed at the start of the second load step, but after a few cycles, the rate of ratchetting changes again. The proposed method has successfully predicted the ratchetting rate for the first and second ratchetting directions. The proposed method in the second load step predicts a negative ratchetting rate for 120 cycles, then the direction of the ratchetting rate changes again in a positive direction, in good agreement with the experimental results. For comparison, predictions of other common ratchetting models are also included in . Material constants used for calculations in these examples are summarized in A method for predicting ratchetting strain is proposed. It is shown that as the ratcheting progresses, a trajectory of the origin of stress may be defined in deviatoric stress space. Stresses and back stresses used in the constitutive equations presented here are measured with respect to this frame of reference. To obtain the ratchetting strain at any desired cycle, this model requires only results of a few cycles, making the model very time-efficient. The proposed model is also capable of predicting the change in direction of ratchetting strain in multi-step loading. A number of numerical examples, including uniaxial and multiaxial loading, are solved and the results compared with experimental results. To examine the merits of the present model in the second load step, in the final example the proposed method has been compared with other models, including those of Xia-Ellyin Response surface and failure probabilityReliability analysis of 500 MWe PHWR inner containment using high-dimensional model representationIn this paper, uncertainty analysis of Indian 500 MWe Pressurized Heavy Water Reactor (PHWR) subjected to an accidental pressure is carried out using a computational tool based on High Dimensional Model Representation (HDMR) that facilitates lower dimensional approximation of the original high dimensional implicit limit state/performance function. The method involves response surface generation of HDMR component functions, and Monte Carlo simulation. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. It is very efficient formulation of the system response, if higher-order variable correlations are weak, allowing the physical model to be captured by first few lower-order terms. Once the approximate form of the original implicit limit state/performance function is defined, the failure probability can be obtained by statistical simulation. Reliability estimates of PHWR inner containment subjected to an internal pressure exceeding the design pressure, considering three stages of progressive failure prior to collapse are presented.Response surface and failure probabilitystrain corresponding to maximum compressive stress of concreteYoung’s modulus of elasticity of reinforcement barYoung’s modulus of elasticity of prestressed tendonultimate tensile stress of prestressed tendonapproximation of original limit state/performance function, g(x)stiffening parameter: ratio of failure strain to elastic strain in tensionsimulation size in Monte Carlo simulationmoving least squares interpolation functionstandard deviation of input random variable icumulative distribution function of standard Gaussian random variableIndia’s current indigenous nuclear power program is based on the Pressurized Heavy Water Reactor (PHWR) Typically, a structural/mechanical component has several failure modes and one can perform reliability analysis corresponding to each of these failure modes. Identification of significant failure modes, thus, constitutes an important aspect of reliability analysis. Uncertainties in structural geometry specification and loads play significant role in the safety of structures and need to be considered in reliability analysis.This paper explores the potential of a new class of computational methods, referred to as High Dimensional Model Representation (HDMR) The paper is organized as follows. Section portrays the structural failure stages of PHWR IC. Section presents the critical locations of PHWR IC. Section presents the random variables considered. Section describes the methodology adopted. Section presents the reliability estimates of PHWR IC subjected to internal pressure exceeding the design pressure, considering three stages of progressive failure prior to collapse. Section presents general discussion on the observed results. Finally, Section provides summary and conclusions of the present study.Over-pressurization of PHWR IC may occur due to the following reasons.Loss of coolant accident (LOCA) due to rupture of the header;Ultimate structural failure of the double containment system occurs sequentially in different stages as depicted in . Due to the over-pressurization of IC, small cracks will form, which further develop into large crack openings. Subsequently debonding of the rebars or tendons occurs, which leads to leakage of the radioactive materials into annulus. With further increase in the annulus pressure high altitude radioactive release through stack and/or cracking of OC occurs.Modeling details of the geometry, materials and loads adopted in finite element (FE) numerical model of PHWR IC are given below.Indian 500 MWe PHWR containment is composed of circular base slab, an upright cylindrical IC and OC walls and torispherical dome for both walls. The dome thickness of OC wall varies from 150 mm at the apex to 610 mm at the springing line (i.e. at the junction of the dome and the cylindrical wall). Similarly, the dome thickness of IC wall varies from 650 mm at the apex to 750 mm at the springing line. IC of PHWR reactor building, which is a pre-stressed concrete structure with cylindrical wall and torispherical dome, is modeled in ADINA is modeled since the geometry and loading are symmetric. Symmetric boundary conditions are applied. Further, only the portion of structure above the raft is considered in the analysis. shows FE discretization details of important substructures; the cylindrical wall with opening (), and the dome region with steam generator (SG) opening (Hypo elastic material model, based on uniaxial stress–strain relationship that is generalized to take into account the biaxial and triaxial stress conditions, is adopted . Hypo elastic material model contains the following three basic features to describe the concrete behavior:Non-linear stress–strain relationship including strain softening in compression.Failure envelop that defines cracking in tension and crushing in compression.Strategy to model the post-cracking and crushing behavior of the concrete.Bilinear elastic–plastic material model with the post-yield modulus as a fraction of the elastic modulus is used for the reinforcing steel and prestressed tendons. Material properties used Maximum compressive stress (fck) = 60 MPaStrain corresponding to maximum compressive stress (εc) = 0.002Ultimate compressive strain (εu) = 0.0035Ultimate compressive stress (σc) = 42 MPaYoung’s modulus of elasticity (Est) = 2.1×105 |
MPaSectional area of prestressing cable (Aten) = 2470 × 10−6 |
m2Young’s modulus of elasticity (Eten) = 2.1 × 105 |
MPaUltimate tensile stress (σuten) = 1950 MPaInitial strain in hoop cable = 5.07 × 10−3Initial strain in vertical cable = 6.88 × 10−3Initial strain in dome cable = 5.06 × 10−3Prestressing force in the tendons is applied by introducing an initial strain. Internal pressure is gradually increased to an ultimate value as shown in . Effect of dead load is also considered in the analysis. In the analysis minor live loads and localized load effects (e.g., reaction from the secondary system, creep and shrinkage) are ignored. Since temperature rise due an accident is relatively of short duration and as the concrete is slow to absorb heat, the forces resulting from temperature variations during an accident are likely to have very little influence on the containment structural elements. Therefore, the temperature effects due to an accident are not considered in the analysis Six critical locations are identified through a sample study and are postulated by Bhabha Atomic Research Centre, India depicts the critical locations of PHWR IC.In the reliability analysis of PHWR IC, compressive strength of the concrete, yield strength of the reinforcing steel and prestressed tendons, and the over-pressurization pressure are considered as random variables, details of which are given below. Mean values of the material are presented in section 3.2.Compressive strength of the concrete fck is assumed to follow normal distribution (mean value of 60 MPa) with coefficient of variation (COV) of 0.14 Yield strength of the reinforcement bar fyst is assumed to follow normal distribution (mean value of 415 MPa) with COV of 0.10 Yield strength of the prestressed tendon fyten is assumed to follow normal distribution (mean value of 1670 MPa) with COV of 0.10 Pressure due to over-pressurization p is assumed to be normally distributed The fundamental principle underlying the HDMR is that, from the perspective of the output/response, the order of the correlations between the independent variables will die off rapidly. This assertion does not eliminate strong variable dependence or even the possibility that all the variables are important. Various sources Evaluating the input-output mapping of the system generates HDMR. This is achieved by expressing system response as hierarchical, correlated function expansion of mathematical structure and evaluating each term of the expansion independently. One may show that system response that is a function of N input variables, g(x)=g(x1,x2,…,xN), can be expressed as summands of different dimensions:g(x)=g0+∑i=1Ngi(xi)+∑1≤i1<i2≤Ngi1i2(xi1,xi2)+…∑1≤i1<…<il≤Ngi1i2…il(xi1,xi2,…,xil)+…+g12,…,N(x1,x2,…,xN),where g0 is a constant term representing the mean response of g(x). The function gi(xi) describes the independent effect of variable xi acting alone, although generally nonlinearly, upon the output g(x). The function gi1i2(xi1,xi2) gives pair correlated effect of the variables xi1 and xi2 upon the output g(x). The last term g12…N(x1,x2,…,xN) contains any residual correlated behavior over all of the system variables. Usually the higher order terms in Eq. The expansion functions are determined by evaluating the input-output responses of the system relative to the defined reference point c={c1,c2,…,cN} along associated lines, surfaces, subvolumes, etc. (i.e. cuts) in the input variable space. This process reduces to the following relationship for the component functions in Eq. gi1i2(xi1,xi2)=g(xi1,xi2,ci1i2)−gi1(xi1)−gi2(xi2)−g0,where the notation g(xi,ci)=g(c1,c2,…,ci−1,xi,ci+1,…,cN) denotes that all the input variables are at their reference point values except xi. The g0 term is the output response of the system evaluated at the reference point c. The higher order terms are evaluated as cuts in the input variable space through the reference point. Therefore, each first-order term gi(xi) is evaluated along its variable axis through the reference point. Each second-order term gi1i2(xi1,xi2) is evaluated in a plane defined by the binary set of input variables xi1,xi2 through the reference point, etc. The process of subtracting off the lower order expansion functions removes their dependence to assure a unique contribution from the new expansion function.Considering terms up to first-order in Eq. yields first-order HDMR approximation of g(x) asg˜(x)=∑i=1Ng(c1,…,ci−1,xi,ci+1,…,cN)−(N−1)g(c).It can also be noted that, compared with FORM and SORM which retains only linear and quadratic terms, respectively, first-order HDMR provides more accurate approximation g˜(x) of the original implicit limit state/performance function g(x) is exact along any of the cuts, and the output response g(x) at a point x off of the cuts can be obtained by following the procedure in step 1 and step 2 below:Step 1: Interpolate each of the low dimensional HDMR expansion terms with respect to the input values of the point x. For example, consider the first-order component function g(xi,ci)=g(c1,c2,…,ci−1,xi,ci+1,…,cN). Suppose for xi=xij, function valuesg(xij,ci)=g(c1,…,ci−1,xij,ci+1,…,cN);j=1,2,…,n,are given at n(=3,5,7or9) equally spaced sample points μi−(n−1)σi/2, μi−(n−3)σi/2,…, μi,…,μi+(n−3)σi/2, μi+(n−1)σi/2 along the variable axis xi through the reference point c. μi and σi are respectively the mean and standard deviation of the variable axis xi. The function value for arbitrary xi can be obtained by the MLS g(xi,ci)=∑j=1nϕj(xi)g′(c1,…,ci−1,xij,ci+1,…,cN),{g′(xi1,ci)⋮⋮g′(xin,ci)}=[ϕ1(xi1)ϕ2(xi1)⋯ϕn(xi1)⋮⋮⋮⋮⋮⋮⋮⋮ϕ1(xin)ϕ2(xin)⋯ϕn(xin)]−1{g(xi1,ci)⋮⋮g(xin,ci)}.The interpolation functions ϕj(xi) can be obtained using the MLS interpolation scheme. By using Eq. , gi(xi) can be generated if n function values are given at corresponding sample points. The same procedure shall be repeated for all the first-order component functions, i.e., gi(xi);i=1,2,…,N.Step 2: Sum the interpolated values of HDMR expansion terms from zeroth-order to the highest order retained in keeping with the desired accuracy. This leads to first-order approximation of the function g(x) asg˜(x)=∑i=1N∑j=1nϕj(xi)g′(c1,…,ci−1,xij,ci+1,…,cN)−(N−1)g0.If n is the number of sample points taken along each of the variable axis and s is the order of the component function considered, starting from zeroth-order to l-th order, then total number of function evaluation for interpolation purpose is given by, ∑s=0l(N!(n−1)s)/((N−s)!s!) which grows polynomially with n and s. As a few low order component functions of HDMR are used, the sample savings due to HDMR are significant compared to traditional sampling. Hence uncertainty analysis using HDMR relies on an accurately reduced model being generated with small number of full model simulations. An arbitrarily large sample Monte Carlo analysis can be performed on the outputs approximated by HDMR which result in the same distributions as obtained through the Monte Carlo analysis of the full model, if higher order cooperative effects are negligible. provides first-order HDMR approximation g˜(x) of the original implicit limit state/performance function g(x) using the MLS interpolation functions, constant g(c) term and first-order g(c1,…,ci−1,xij,ci+1,…,cN) terms. Therefore the failure probability PF can be easily estimated by performing MCS on first-order approximation g˜(x) of the original implicit limit state/performance function g(x) and is given bywhere xi is ith realization of X, is the sampling size, I[.] is a deciding function of fail or safe state such that I=1, if g˜(xi)<0 otherwise zero. Flow diagram for the computational process of first-order HDMR approximation and the failure probability PF estimation by MCS is shown in . Reliability index β corresponding to the failure probability PF can be obtained bywhere Φ(•) is the cumulative distribution function of standard Gaussian random variable.Since first-order HDMR approximation leads to explicit representation of the original implicit limit state/performance function, MCS can be conducted for any sampling size. The total cost of original function evaluation entails maximum of (n−1)×N+1 by the present method using first-order HDMR approximation. Sampling scheme for first-order HDMR approximation of a function having one variable (x) and two variables (x1 and x2) is shown in In analyzing PHWR IC subjected to an internal pressure exceeding the design pressure, the following three stages of progressive failure prior to collapse have been considered: (a) crack initiation on the inner and outer surfaces of PHWR IC The limit state/performance function for the crack initiation due to over pressurization is taken asThe original implicit limit state/performance function in Eq. is approximated using the first-order HDMR approximation presented in at each of the six identified critical locations (shown in ). In this study the reference point c is taken as mean values of the random variables considered. Since in this case fck, fyst, fyten, and p are considered as random variables, N=4. In addition, in this case n=7 equally spaced sample points along each of the variable axis are adopted for the response surface generation using the first-order HDMR approximation described above. Therefore total number of ADINA FE analysis required is 25.At the six identified critical locations the probability of crack initiation is estimated by performing MCS on the first-order HDMR approximation of the original implicit limit state/performance function. presents the failure probabilities on the inner and outer surfaces of each of the six identified critical locations.The limit state/performance functions considered for yielding of the reinforcing steel and prestressed tendons are also defined as in Eq. , except that fct is replaced with fyst and fyten, respectively. Again the original implicit limit state/performance functions for yielding of the reinforcing steel and prestressed tendons at each of the six identified critical locations are approximated using the first-order HDMR approximation by taking the reference point c as mean values of the random variables and 25 ADINA FE analysis. The failure probability due to exceedance of yield strength of the reinforcing steel and prestressed tendons at the ultimate pressure is estimated by performing MCS on the first-order HDMR approximation of the original implicit limit state/performance function. , respectively presents the failure probabilities due to exceedance of yield strength of the reinforcing steel and prestressed tendons at the ultimate pressure at each of the six identified critical locations.The observations from the present investigation are summarized in the following:Failure due to crack initiation on the outer surface is most dominant in the cylindrical region (PF=1.9×10−8). Subsequent dominant regions are the bottom of ring beam (BRB) (PF=2.91×10−8), the top of ring beam (TRB) (PF=1.28×10−9) and the wall discontinuous region (PF=1.42×10−9).Failure due to crack initiation on the outer surface is most dominant in the BRB (PF=1.08×10−8). In other regions the failure probability is negligibly small (PF<1.0×10−10).There is no failure event due to vertical rebar yielding at the design pressure.Failure due to vertical rebar yielding at the ultimate pressure is most dominant on the outer surface of the wall discontinuous region (PF=1.92×10−6). Subsequent dominant regions are the BRB (PF=2.81×10−6), the TRB (PF=1.46×10−7) and the cylindrical wall (PF=1.56×10−7).There is no failure event due to circumferential rebar yielding at the design pressure.Failure due to circumferential rebar yielding at the ultimate pressure is most dominant in the dome region around SG Opening (PF=3.92×10−5). Subsequent dominant regions are the dome (PF=4.2×10−7) and the cylindrical wall (PF=6.45×10−7).Failure due to vertical tendon yielding at the ultimate pressure is most dominant on the inner face of the wall discontinuous region (PF=3.24×10−5). Subsequent dominant regions are the outer surface of the wall discontinuous region (PF=2.8×10−6), the cylindrical wall (PF=8.08×10−6), the BRB (PF=8.08×10−6) and the TRB (PF=1.2×10−7).Failure due to circumferential tendon yielding at the ultimate pressure is most dominant in the dome region (PF=2.8×10−7). Subsequent dominant regions are the cylindrical wall (PF=3.52×10−7), the TRB (PF=3.65×10−7) and the BRB (PF=5.3×10−7).In structural reliability assessment of real life problem, the limit state/performance functions are most often specified implicitly through FE code. This paper explored the potential of HDMR based computational tool for predicting the failure probability of PHWR containment subjected to random loads and material properties. It utilized the excellent properties of HDMR for multivariate function approximation and moving least square as interpolation scheme. Due to small number of original function evaluations, the proposed HDMR approximations are very effective, particularly when response evaluation entails costly finite-element, or other numerical analysis.Superdurable fiber-reinforced composite enabled by synergistic bridging effects of MXene and carbon nanotubesThe corrosion of fiber-reinforced polymer (FRP) composite has given rise to a tricky problem with implications in many fields including civil, aerospace, and environment. The degraded mechanical performance of FRP caused by corrosion usually results from surface and interface corrosion, which is especially problematic in the humid and alkali environment. Herein, basalt fiber reinforced polymer (BFRP) reinforced with 3D MXene Ti3C2Tx/carbon nanotubes (CNTs) nanofillers with long-term stability was fabricated and the reinforced mechanism was investigated experimentally. Results show that the synergistic effect of MXene/CNTs can obviously enhance the interfacial adhesion between adjacent fiber yarns and increase the tensile strength and flexural strength of BFRP composite by 53.5% and 43.2%, with pure BFRP as a comparison. The effectiveness of MXene/CNTs to act as corrosion inhibitor was evaluated by alkali immersion testing. After 120 days of immersion in alkali solution, bare BFRP had a significant increase in surface defeats and roughness, which resulted in remarkable reduction in flexural strength. In contrast, MXene/CNTs-BFRP composite exhibited negligible changes in both surface roughness and flexural strength. Therefore, the present work provides the new hybrid carbon nanofillers with a unique structure, which makes FRP capable enough to serve in more complex environment.Fiber-reinforced polymer (FRP) is an advanced material central to applications from automobile and aerospace, to navigation and construction owing to their low-density and high specific strength, stiffness, toughness properties []. Despite the tremendous convenience they bring to our daily life, the major bottlenecks circumventing the large-scale utilization of FRP-based equipment lie in long-term service safety []. The degraded performance of FRP in alkali and humid concrete is especially problematic. Water and ions corrode epoxy resin and fibers through an ionic diffusion and exchange process which resulting in complex chemical and physical changes on the surface and interfaces. Consequently, the microstructure of fiber fabric is broken and slight cracks appear inside of resin, gradually leading to significant degradation and strength reduction of FRP materials [Various methods have been proposed to enhance anti-corrosion properties and/or improve the fiber matrix adhesion, including coupling agent coating, chemical or plasma treatment, growth of nanoparticles, among which matrix modification techniques have been mostly adopted in practice. In particular, the emerging two-dimensional (2D) materials offer opportunities for preparing high-performance polymeric composites []. The 2D feature and high mechanical properties of such fillers of plane structure could not only enhance the mechanical properties of polymer composites, but also minimize the permeation of corrosive media (such as H2O, O2 and OH−) [MXenes, a newly class of 2D transition metal carbides, carbonitrides, and nitrides, has emerged and drawn significant attention since the first discovery in 2011 []. Among the prevailing candidates, Ti3C2Tx is the most widely studied one and has shown promising prospects in diverse fields such as interface enhancement [], electromagnetic interference (EMI) shielding []. Moreover, Ti3C2Tx is being explored as an additive material for composites requiring resistance to corrosion, friction, EMI, etc., owing to its excellent mechanical properties, chemical barrier properties, and abundant surface groups –Tx (-O, –F, –OH). For example, Ti3C2Tx nanosheets have been adopted to improve interaction and surface wettability of the poly-pyridobisimidazole fiber/epoxy. Meanwhile, the UV and hydrothermal aging resistance of the grafted fibers have been greatly enhanced []. Another study used a PAI/Ti3C2Tx composite sizing to modify interface for CF/polyetheretherketone composites and found that the interfacial adhesion and EMI shielding performances have increased simultaneously. Furthermore, relying on characteristic structure and nature of Ti3C2Tx [], abundant Lewis acid and hydroxyl groups on the surface could promote the confined transport of water and ions. Thus Ti3C2Tx and its composites such as Ti3C2Tx/PANI [], have been demonstrated to resist corrosion. However, the stacking problem of 2D nanofillers (e.g. Ti3C2Tx) in matrix is extremely problematic and there is no in-depth discussion and strategy on how Ti3C2Tx composite improve the anti-corrosion properties of fiber-based composites. It is urgent to design more corrosion-resistant FRP materials and understand the enhanced mechanism. Among various modified methods, increasing the interlayer spacing through the intercalation of pillaring materials has been proved to be an effective way to prevent the usual restacking of 2D nanosheets. For instance, Cai et al. [] have prepared Ti3C2Tx MXene/CNT sensors through a layer-by-layer spray coating technique with extraordinary sensitivities. Xu et al. [] proposed an ultra-stable and washable strain sensor by embedding a coupled composite film of CNTs and Ti3C2Tx into polydimethylsiloxane (PDMS) matrix. Fang et al. [] introduced CNTs/PANI into Ti3C2Tx nanosheets and found that the EM shielding performance was enhanced. As these studies show, introducing 1D CNTs into 2D MXene nanosheets with a hybrid structure might be an efficient approach to fabricate more corrosion-resistant FRP materials.Herein, we investigated the colloidal assembly of Ti3C2Tx/CNTs materials, with a primary goal of constructing a 3D hybrid structure for anti-corrosion basalt fiber-reinforced polymer (BFRP) composite. The incorporation of CNTs into the Ti3C2Tx prevented the usual restacking of 2D nanosheets and created more contact areas between nanofillers with resin. In addition, the interfacial adhesion between adjacent fiber yarns has been greatly improved owing to the synergistic effect of 1D-CNTs and 2D Ti3C2Tx. The effectiveness of the addition of MXene/CNTs to BFRP was evaluated by immersion in alkali solution for up to 120 days. Results showed the MXene/CNTs hybrid inhibitor effectively enhanced the mechanical properties and while maintaining morphology which confirmed the significance of MXene/CNTs hybrid in corrosion protection. This work not only put forward an effective and facile method to fabricate FRP composite with excellent anti-corrosion performance, but also broadened the application of MXene.The MAX (Ti3AlC2, 98%, 200 mesh) was purchased from Jilin 11 technology co. Ltd. Multi-wall carbon nanotubes (MWCNTs) were purchased from Nanjing XFNANO Technology Co. Ltd. The outer dimeter and length of MWCNTs were 5–15 nm and 10–30 μm, respectively. Hydrochloric acid (HCl), sulfuric acid (H2SO4) and nitric acid (HNO3) were purchased from Sinopharm Chemical Reagent Co., Ltd. Sodium hydroxide (NaOH), potassium hydroxide (KOH), and calcium hydroxide (Ca(OH)2) were purchased from Sinopharm Chemical Reagent Co., Ltd. The raw CNTs were refluxed at 60 °C for 3 h in the mixture of H2SO4 and HNO3 solution (v/v = 3:1) and then filtered and dried at 80 °C for 12 h to obtain acidified CNTs. Lithium fluoride (LiF), cetyl trimethyl ammonium bromide (CTAB) and acetic acid were purchased from Shanghai Macklin Biochemical Technology Co., Ltd. The resin Epoxy 51 and harder were adopted to fabricate FRP laminates, which were obtained from Wuxi Resin Co. Ltd. The viscosity of thermosetting epoxy resin (E51) and harder (JH5531) was 1000 mPa s and 80–150 mPa s (25 °C), respectively. The Tg of the pristine epoxy was about 60.2 °C. Unidirectional basalt fiber fabrics were chosen as the reinforcement of FRP laminates and obtained from Xika Composite Materials Technology Co., Ltd. The area density and normalized thickness of fabrics were 300 g/m2 and 0.15 mm. The fiber fabrics were washed by anhydrous ethanol by sonication to eliminate the surface sizing and then immersed in acetic acid (1.0 mol/L) for 2 h. Finally, the fibers were rinsed with deionized water several times until the surface pH of fibers was close to 7 followed by drying at 80 °C for 12 h.MXene was prepared by etching the MAX phase. Typically, 1.0 g of LiF was slowly added into 10 mL of 9 M HCl solution until powders were totally dissolved, then 1.0 g of MAX Ti3AlC2 powder was dispersed in the mixed solution under magnetic stirring at 45 °C for 24 h. After that, the obtained mixture was centrifuged and washed several times until the pH value of supernatant reached around 5. The final supernatant was collected and dried at 60 °C for 12 h.The MXene powders with various ratios were dispersed in ethanol using probe sonication for 15 min. After that, CTAB was added into the MXene solution (mass ratio of CTAB/MXene = 1:5). To prepare the MXene/CNTs hybrid, the acidified CNTs was also dispersed into the mixed solution to get the MXene/CNTs hybrid.The neat epoxy and epoxy nanocomposites containing MXene (1 wt%), acidified CNTs (1 wt%), MXene/acidified CNTs (0.25–0.75 wt%), MXene/acidified CNTs (0.50–0.50 wt%), and MXene/acidified CNTs (0.75–0.25 wt%) were prepared using the same process. MXene-epoxy composite, for example, was prepared by adding MXene suspension into resin under mechanical stirring for 30 min. The solvent in the resin mixture was subsequently evaporated at 60 °C and under low pressure through rotary evaporator to obtain MXene-epoxy composite. The curing agent (mass ratio of resin/curing agent = 2:1) was then mixed with MXene-epoxy composite under mechanical stirring.The BFRP laminate composites were manufactured by a vacuum-assisted resin-transfer molding (VaRTM) process []. Five layers of basalt fiber fabrics were stacked and placed over a PTFE sheet on the surface of a glass mold. Two pieces of peel plies were put at the top and bottom of the fabrics layers to prevent sticking. The infusion mesh was added on the top of the upper peel ply. The entire package was then sealed in a vacuum bag with two-sided butyl tape. After that, a vacuum pump was used to draw out the air trapped inside the mold to establish a vacuum environment. Under the vacuum pressure, the mixture of the degassed resin and curing agent was infused into the package. The resin composite was cured at room temperature for 24 h and then put in a vacuum oven at 60 °C for 12 h. Finally, BFRP with different contents of MXene and CNTs were prepared. The mass ratio of MXene (1 wt%), acidified CNTs (1 wt%), MXene/acidified CNTs (0.25–0.75 wt%), MXene/acidified CNTs (0.50–0.50 wt%), and MXene/acidified CNTs (0.75–0.25 wt%) were denoted as MBFRP, CBFRP, M0.25C0.75, M0.50C0.50, and M0.75C0.25, respectively.The morphology investigations of BFRP and nanomaterials were examined with scanning electron microscope (SEM, Zeiss SUPRA 55 SAPPHIRE). The chemical structure of samples was characterized by Fourier transform infra-red spectroscopy (FT-IR, Thermo Fisher Scientific, USA) and Raman spectroscopy. X-ray diffractometer (XRD) characterization was performed using a X’PERT instrument with Cu Kα radiation (45 kV, 50 mA). The surface chemical analysis of MXene and acidified CNTs was obtained in an X-ray photoelectron spectroscopy system (XPS, Model K-Alpha, Thermo Scientific, USA). Atomic force microscopy (AFM, Dimension Fastscan, Bruker, USA) was employed to measure the thickness of the MXene on the silicon wafer. Dynamic contact angle of different basalt fibers coated with nanofillers were tested through a dynamic contact angle meter (DCAT21, Data Physics Instruments, Germany). Polar deionized water was used as testing liquids.The mechanical properties of FRP samples were evaluated using a universal test machine (DHT-800, Hengyi Precision Instrument Co. Ltd., China). The tensile properties of samples were tested according to ASTM . Typically, the dimensions of specimens were 200 mm × 15 mm × 1.2 mm and the crosshead speed was set as 2 mm/min. The tensile strength (σ) and modulus (E) of the samples were calculated as follows:Where P was the tensile load, A was the average cross-sectional area, Δσ and Δε were the stress and strain change for the linear stage of the tensile curve, respectively.The flexural performance of samples was tested in three-point bending mode according to ASTM . The dimensions of specimens were 60 mm × 13 mm × 1.2 mm and the crosshead speed was set as 5 mm/min. The flexural strength (σ) and modulus (E) of the samples were calculated as follows:Where P, L, b, d, and m were flexural load, support span, specimen width, specimen depth, and initial slope of the load-displacement curve, respectively.The moisture absorption properties of the samples were calculated according to ASTM D 5229 by the following equation:Where w (%) is the weight gain, wt is the weight at time t, and w0 is the dry weight at t = 0.Dynamic mechanical analysis (DMA) of samples was carried out on a dynamic mechanical thermal analysis machine (Q800, TA Instruments Co., USA). The test mode of DMA was in a single cantilever mode at a frequency of 1 Hz. The dimensions of specimens were 50 mm × 8 mm × 1.2 mm. The temperature varied from room temperature to 140 °C with a heating rate of 5 °C/min. Storage modulus (Eʹ), loss modulus (Eʺ), and loss factor (tan δ), of the samples were recorded. demonstrated the preparation process of the MXene/CNTs-BFRP composite, which began with the fabrication of MXene/CNTs hybrids by assembly technology and succedent VaRTM manufacturing process. First, MXene Ti3C2Tx sheets were obtained from MAX Ti3AlC2 phase powders by selectively chemical etching the Al layers, as reported previously []. Simultaneously, CNTs were treated with acid solution to modify surfaces with functional groups (-COOH, –OH). It's noteworthy that both Ti3C2Tx and acidified CNTs (ACNTs) were negatively charged because of the surface functional groups [], when cationic surfactant CTAB was added into the MXene solution, strong interactions were established between MXene and CNTs through electrostatic attraction, which could prevent the self-restacking of 2D nanosheets or 1D nanotubes []. After pretreatment, MXene/CNTs composites were mixed with epoxy resin, followed by heating to 60 °C and under low pressure through the rotary evaporator to remove residual solvent. Finally, basalt fiber fabrics were stacked to achieve desired thickness, followed by a VaRTM manufacturing process as MXene/CNTs resin composites pumped into mold and cross-linked.The combination of MXene and CNTs was confirmed by SEM analysis and could be explained by a well-studied mechanism of self-assembly. Typically, the multi-layered MXene prepared by etching MAX phase showed an accordion-like structure and few-layered MXene exhibited a typical 2D nanosheet morphology (). The plane structure of the MXene nanosheets was further confirmed by AFM. As indicated in f, MXene had a large lateral dimension of over 3 μm and thickness of about 2.3 nm. After combination with ACNTs, the hybrids exhibited a grass like structure, where CNTs were randomly distributed over the basal plane of MXene (d). The self-assembled MXene and CNTs composites were obtained through the electrostatic interactions, π-π conjugation and hydrogen bond, which not only helped CNTs to get absorbed and stick to MXene pale, but also effectively prevented the restacking of MXene nanosheets, as illustrated in g. It was worth mentioning that the 3D unique structure constructed by nanosheets and nanotubes could benefit the dispersion in matrix, which would be discussed later.To gain more insight about the structure of the samples, XRD characterization was performed. As shown in a, the diffraction peaks of MXene at 2θ = 8.82°, 18.23°, 27.44°, 41.77°, and 60.55° matched well with the peaks of the (002), (004), (008), (0012), and (110) planes, respectively. Notably, the diffraction peak of MAX in the (002) plane at 9.70° became broader and left shifted to a lower degree of 8.82° in MXene, demonstrating the successful extraction of Al layers, and the interlamellar spacing between the MXene was about 1.01 nm according to Scherrer formula. For ACNTs, the prominent peak at scattering angle of 2θ = 25.99° was observed.Apart from crystal structure, chemical structures of nanofillers played an important role in combining with matrix. b represented the FT-IR curves of ACNTs. Pronounced peaks in 3391 cm−1, 1703 cm−1, 1549 cm−1, 1226 cm−1, 1157 cm−1 and 1052 cm−1 ascribed to O˗H stretching vibrations, CO stretching vibrations of the –COOH groups, CC stretching vibrations, C˗O vibrations, C–O–C stretching vibrations, and C–O stretching vibrations, respectively. showed the homogeneous dispersion of MXene and CNTs before and after acid treatment, which further indicated the abundant hydrophilic functional groups (such as –OH) on the surface. The oxygen-containing functional groups on MXene and ACNTs could effectively improve the dispersion stability and form a strong interaction between nanofillers and epoxy resin at molecular level [c showed the Raman spectra of the as-prepared samples, the modes of MXene at 200 and 706 cm−1 were mainly ascribed to the A1g symmetry out-of-plane vibrations of Ti and C atoms, while the modes at 385 and 624 cm−1 were assigned to the Eg groups vibrations, including in-plane (shear) modes of Ti, C and surface functional group atoms. Moreover, two broad bands appeared at 1351 and 1591 cm−1 of CNTs were characteristics for the D and G bands of graphitic carbon.The surface chemical states were analyzed by XPS measurements. d showed the overall spectra, it confirmed that the existence of Ti, C, O, and F in MXene nanosheets. The peak related to O in ACNTs further indicated successful introduction of the oxygenic groups on surface, which benefited the dispersion in resin. High-resolution spectra of O 1s core levels of MXene and ACNTs were shown in e and f and , respectively. Two peaks in the spectrum of MXene at 529.1 eV and 531.8 eV corresponded to TiO2 and C–Ti–O, respectively. In addition, the peaks of ACNTs at 530.9 eV and 532.3 eV could be attributed to CO and C–O, respectively. In conclusion, all the above results proved that 2D MXene/1D CNTs hybrids with unique 3D structure and abundant functional groups had been prepared successfully.Note that the dispersion of nanofillers in resin was extremely important for BFRP, which greatly influenced the performance of the service, the morphology of epoxy and its composites were firstly analyzed by SEM. As shown in b and c). It was worth mentioning that there were self-staking and aggregations in both MXene-epoxy and CNTs-epoxy composites, which was mainly caused by strong van der Waals force and would limit reinforcement efficiency []. Intriguingly, the SEM results of MXene/CNTs-epoxy demonstrated the well dispersion of nanofillers, and the MXene/CNTs hybrids were held tightly by the matrix. It had been confirmed that 1D CNTs could act as bridges in matrix with the respective pull-out behavior, thus the CNTs network incorporated in the MXene nanosheets not only prevented the usual restacking of 2D MXene but also created more contact area between nanofillers with resin []. Besides, elemental mapping of MXene-epoxy and MXene/CNTs-epoxy were exhibited in , respectively, further confirmed that there were self-staking and aggregations of MXene in resin, which was caused by strong van der Waals force and would limit reinforcement efficiency. The addition of CNTs effectively prevented the usual restacking of MXene nanosheets in matrix. Accordingly, XRD was applied to study the MXene/CNTs-epoxy composites. All the samples exhibited wide peaks ranging from angles of 15°–25°, which belonged to epoxy matrix. In addition, the weak peak of (002) plane of MXene could be observed in both MXene epoxy and MXene/CNTs-epoxy composite, demonstrating the well dispersion of nanofillers in matrix.In the FRP, the polymer matrix was mainly applied to give shape to specific structure, protect the embedded fabric from environmental corrosion, and transfer load to inner fibers. Here, VaRTM manufacturing process was employed to inject resin into mold to fabricate BFRP lamina. As shown in g and h and , the mixture of the degassed resin and curing agent were infused into the package under the vacuum pressure, which could eliminate air bubbles and achieve uniform thickness (pure basalt fiber was shown in , the diameter was about 14 μm). The cross section and surface morphology of MXene/CNTs-BFRP were shown in i and j, respectively. It could be seen that basalt fibers were embedded tightly in matrix composites, which mainly attributed the synergetic effect for the MXene/CNT/epoxy composite.The thermomechanical properties of BFRP and MXene/CNTs-BFRP were investigated by DMA test, from which the storage modulus (Eʹ), and loss modulus (Eʺ), were calculated. The results were plot in . In DMA technique, storage modulus was related to the ability of material to return or store energy while loss modulus was related to the ability of material to dissipate energy []. As shown, the MXene/CNTs-BFRP demonstrated higher storage modulus, which could be ascribed to the synergetic effect of MXene and CNTs. The addition of CNTs not only prevented the agglomeration of MXene but also increased the interfacial contact area between MXene and resin, thus restricted the segmental movement of polymer chains. Moreover, the interfacial load between the matrix and nanomaterials can be effectively transferred. The glass transition temperature (Tg) was determined from the peak position of the tan δ. Note that the Tg of M0.50C0.50 increased significantly compared with that of neat BFRP, indicating MXene and CNTs effectively enhanced the thermal stability of BFRP. On the basis of the results obtained, we put forward that the higher Tg resulted from the hybrid structure of MXene/CNTs among epoxy monomers. Besides the structural properties of MXene and CNTs, the abundant functional groups on the materials had a tendency of preferential interaction with epoxy resin which participated in the cross-link reaction with polymer.The mechanical properties of MXene/CNTs-BFRP composites were evaluated at room temperature by three points bending and uniaxial tensile tests. The resulting flexural stress and strain of the BFRP and MXene/CNTs hybrid BFRP laminas were plotted in a and the flexural strength and modulus for each set of laminas were shown in b and c and , respectively. Notably, the MXene/CNTs-BFRP exhibited superior flexural strength and modulus than BFRP, C-BFRP and M-BFRP. Additionally, the flexural strength and modulus of M0.75C0.25 were 43.2% and 17.4% higher than that of base line BFRP. It was undoubted that the synergistic effect of MXene/CNTs played a key part in flexural properties and protected the structure, corresponding enhancement mechanism was shown in e. As was known, the improved effect of carbon nanofillers in matrix was influenced by two major factors, the degree of dispersion and interfacial interaction with polymer chains. Generally, the incorporation of 1D nanofillers CNTs and 2D nanofillers into matrix had a great tendency to restack and decrease the reinforcement effect, which was caused by strong van der Waals force and π-π interactions. Moreover, the aggregations of MXene impeded the flow of matrix during VaRTM process, thus leading to defects and a suboptimal dispersion, further reduced the mechanical properties. Previous studies had reported that CNTs could significantly inhibit the agglomeration of graphene oxide (GO) and create more contact areas with polymer resin. MXene, as a typical 2D material, had a similar structure and functional groups with GO. Accordingly, CNTs could not only prevent the usual restack of MXene, but also serve as bridge for load carrying capacity. With the introduction of 3D MXene/CNTs hybrids, the terminating groups of 2D MXene and 1D CNTs had a great affinity to macromolecules, which benefited for restraining interfacial sliding and debonding in BFRP composite. Clearly, co-existence of MXene and CNTs promoted the stress transfer from the polymer matrix to the nanofillers, and also made the crack propagation path more tortuous. Therefore, the effect of nano-rivet could be strengthened during the stretching, which attributed to the effective stress transfer at the interface between epoxy matrix and nanofillers as well as at the interface between MXene and CNTs []. In addition, micro size MXene could encapsulate the basalt fibers firmly and grass like CNTs anchor itself in polymer matrix simultaneously. As a consequence, the bridging effect could be associated with an increase in flexural properties.Regarding practical use, the tensile performance also needed to be considered. The tensile strength and modulus of BFRP laminas had been evaluated through uniaxial tensile test and the stress-strain curves were shown in d. As shown, the tensile testing results exhibited a linear response to failure. Besides, the MXene/CNTs hybrid BFRP composites clearly outperformed the reference prepared BFRP in terms of strength, modulus and toughness, highlighting the influence of nanofillers. The tensile strength of neat BFRP was found to be σ ≈ 484 MPa and tensile modulus E ≈ 33.4 GPa, both of which agree with other reports. Remarkably, the tensile strength of MXene/CNTs hybrid BFRP laminas was higher than that of the individual or binary components. For example, the tensile strength of M0.75C0.25 was about 743 MPa which showed a substantial increase by ∼53.5% as compared with BFRP. In addition, MXene/CNTs hybrid BFRP laminas showed an increase in tensile modulus, E, over the BFRP from 33.4 ± 2.4 GPa to 34.6 ± 1.3, 35.9 ± 0.9 and 34.0 ± 0.9 GPa for M0.25C0.75, M0.50C0.50, and M0.75C0.25, respectively. It was obvious that the increased modulus could be ascribed to the 3D MXene/CNTs hybrid structure. As illustrated by the proposed models (h), the chemical cross-linked MXene/CNTs act as networked nano-rivet in polymer matrix. The nanofillers were well dispersed in the resin and embedded strongly by the polymer matrix. During the stretching process, the stress was effectively transferred not only at the interface between epoxy matrix and basalt fibers, but also at the interface between nanofillers and matrix, as well as at the interface between MXene and CNTs. As a consequence, the bridging effect could be further enhanced with an increasing tensile properties. From the results of these tests, it could be seen that the hybrid structure of MXene/CNTs endowed high mechanical performance to the BFRP materials, highlighting the influence of synergistic effects between CNTs and MXene.The fracture surfaces perpendicular to the fiber direction for selected FRP specimens tested were investigated by SEM, the overviews were present in g–j. BFRP, as a composite of high modulus basalt fibers embedded into E51 epoxy matrix, featured a predominantly brittle fracture surface (g). The cracks mainly spread at the interface between the fiber and the matrix, resulting in little matrix fragments adhering to fibers. After a high number of fibers fractured and pulled out, some isolated pores were detected in a small part of the crack surface, which further confirmed the local brittle failure. The CBFRP specimen got similar results. As shown in h, a rough surface with fragments, gaps between fibers and matrix, and pores were detected, revealing the poor adhesion between the components. In contrast, MXene/CNTs-BFRP hybrid lamina had a much more improved adhesion. The fibers in the fracture surface were mostly covered by polymer matrix and resin fragments, indicating increased interfacial adhesion which mainly attributed to the synergetic effect of the bi-component nanofillers. The MXene and CNTs decreased the slippage of polymer chains and effectively transferred stress on the interfaces, thus the failure of the matrix appeared to be a mixed brittle and ductile mode. Based on the above results, it was clear that the MXene/CNTs bi-components endowed the BFRP with enhanced interfacial properties and increased the mechanical performance.In practical applications, FRP usually underwent long-term corrosion; thus, a mechanical stable structure was required for the FRP. From the perspective of chemical stability, resin matrix provided a protected layer to fibers and prevented them from corrosion. Thus, an ideal resin matrix, especially for the application in civil engineering, should possess high stability in the alkali environment. In order to simulate harsh civil alkali environment (pH ≈ 13, detailed concentration of chemicals was shown in ), a multicomponent mixed solution was prepared and BFRP laminates were immersed in the solution for 120 days (as shown in b and c showed the percentage of weight gain of the as-prepared BFRPs at strong alkaline solutions. As could be seen, the water uptake process curves of samples could be divided into three stages, which conformed to Fick's diffusion model. Firstly, the surface of laminates contacted solution and the water uptake increased rapidly in a short time. After a period of time, the increased rate of samples gradually became slower, which could be mainly affected by the free volume of polymer chains. With further extending of immersion time, water absorption of FRP got saturated and the water uptake curves tended to be gentle. The water gain percentage of BFRP for 120 d was higher than that of CBFRP and MBFRP, which might be associated with the restriction of polymer chains by nanofillers. The M0.25C0.75 demonstrated outstanding retarding water absorption performance, and maintained a lower water absorption percentage about 1.32 wt% after 120 days. Meanwhile, the water contact angle of basalt fibers coated with nanofillers were evaluated and the results were shown in d. The fibers coated with MXene/CNTs showed a lower angle, indicating improved surface energy and enhanced adhesive properties, which could prevent corrosive liquid from weak interfaces on smooth fibers, thus enhanced the anti-corrosive properties of BFRP composites []. Generally, the dispersion and polarity components were related to the surface roughness and surface functional groups of nanofillers. As a consequence, the MXene/CNTs hybrids not only provided a physical barrier and tortuous diffusion path, but also improved the interfacial properties and effectively prevented corrosive liquid from weak interfaces on smooth fibers. Accordingly, the flexural strength of BFRP and MXene/CNTs-BFRP composites after immersed in alkali solution for 120 d was tested. As shown in e, the MXene/CNTs-BFRP still exhibited superior flexural strength and modulus than BFRP, C-BFRP and M-BFRP. Moreover, compared with initial flexural strength of BFRP, the flexural strength of BFRP in alkali solution for 120 d decreased and remained about 95% of initial strength, while the properties of MXene/CNTs-BFRP composites were quite stable and the strength of M0.75C0.25 remained about 130% of that of initial BFRP, indicating the long-term stable and reliable performance under alkaline condition.To investigate the influence of alkali environment on the laminate composite, the surface morphology of BFRP and MXene/CNTs-BFRP were analyzed. As shown in g and h, the alkali solution had a great influence on BFRP composite while the MXene/CNTs-BFRP exhibited little changes on surface of laminate. As discussed earlier, ions and water corroded epoxy resin and fibers when BFRP laminates were immersed in alkali solution. Consequently, bare BFRP had a significant increase in surface defeats and roughness, microstructure of fiber fabric was broken and slight cracks appeared inside of resin, then gradually leading to significant degradation such as voids and cracks. The addition of MXene not only increased the surface roughness but also decreased the permeation of water molecules, which had been confirmed in other studies [The aging mechanism of BFRP and MXene/CNTs-BFRP laminates could be further illustrated in . Epoxies were a class of thermosetting polymers, which were composed of functional groups with reactive three-membered cyclic ether rings. It was vitally of great significance to maximize its resistance to water to prevent delamination or degradation. Intriguingly, 2D MXene presented outstanding resistance to the permeation of moisture and gases. Permeability was generally affected by volume fraction and degree of dispersion of nanofillers. As was shown in the water uptake test, the decrease of permeation could be ascribed to a longer path with greater tortuosity, thus diffusing species must navigate to permeate the interfaces and fibers. When the laminates were immersed in alkaline solution, the epoxy matrix first contacted with corrosion environment and began to degrade due to the hydrolysis reaction which brought the generation of micro-cracks []. Afterward, water molecules entered into the epoxy matrix through the micro-cracks.Compared with neat matrix, the 2D MXene provided excellent physical barrier against permeation of water molecules and minimized the propagation of cracks. Moreover, the strong chemical bond interaction between nanofillers could effectively restrain the decrease of mechanical properties. Therefore, the degrade of MXene/CNTs-BFRP laminate was milder than that of pure BFRP laminate, leading to maintain higher mechanical performance. Combined with the results in this study, it could be concluded that the MXene/CNTs hybrid effectively slowed down the degradation of FRP composite.In summary, MXene-composited BFRPs with excellent mechanical performances and long-term stability in alkaline environment have been successfully constructed by integrating MXene and CNTs into BFRP composite. The MXene/carbon nanotubes (CNTs) hybrid nanostructure was designed and combined by electrostatic self-assembly, which effectively prevented the self-restacking of MXene layers. Compared with neat BFRP, the MXene/CNTs-BFRP composites exhibited high tensile strength and modulus as well as excellent flexural strength and modulus, owing to the well dispersed hybrid structure of MXene and CNTs. Meanwhile, the enlarged interlayer spacing of MXene and interconnected CNTs networks endowed strong interfacial interaction between the fillers and matrix. The as-prepared MXene/CNTs-BFRP composite also presented low water absorption property and high stability in strong alkaline solution. This work provided a facile and effective way to fabricate high-performance MXene reinforced FRP composite and can be employed for structure application in a harsh environment.The authors declare no conflict of interest.Yue Qian: Conceptualization, Methodology, Investigation, Writing – original draft. Jing Zhong: Supervision, Writing – review & editing. Jinping Ou: Funding acquisition, Supervision, Project administration, Writing – review & editing.We declare that we have no financial and personal relationships with other people or organization that can inappropriately influence our work.The following is the Supplementary data to this article:Supplementary data to this article can be found online at Comparative analysis of poly-glycolic acid-based hybrid polymer starter matrices for in vitro tissue engineeringBiodegradable scaffold matrixes form the basis of any in vitro tissue engineering approach by acting as a temporary matrix for cell proliferation and extracellular matrix deposition until the scaffold is replaced by neo-tissue. In this context several synthetic polymers have been investigated, however a concise systematic comparative analyses is missing. Therefore, the present study systematically compares three frequently used polymers for the in vitro engineering of extracellular matrix based on poly-glycolic acid (PGA) under static as well as dynamic conditions. Ultra-structural analysis was used to examine the polymers structure. For tissue engineering (TE) three human fibroblast cell lines were seeded on either PGA-poly-4-hydroxybutyrate (P4HB), PGA-poly-lactic acid (PLA) or PGA-poly–caprolactone (PCL) patches. These patches were analyzed after 21 days of culture qualitative by histology and quantitative by determining the amount of DNA, glycosaminoglycan and hydroxyproline. We found that PGA-P4HB and PGA-PLA scaffolds enhance tissue formation significantly higher than PGA-PCL scaffolds (p < 0.05). Polymer remnants were visualized by polarization microscopy. In addition, biomechanical properties of the tissue engineered patches were determined in comparison to native tissue. This study may allow future studies to specifically select certain polymer starter matrices aiming at specific tissue properties of the bioengineered constructs in vitro.During the last years, the interdisciplinary field of tissue engineering (TE) has emerged as a platform for the development of biological substitutes. The overall goal is the repair and/or regeneration of tissues or organs to resolve major health related concerns in humans. Multiple disciplines, such as cell biology, biomaterial research and biomedical engineering have contributed to the advances of tissue engineering technologies. Any tissue engineering approach is composed of three major components: (1) cells, (2) biocompatible scaffolds, and (3) suitable biochemical (e.g. growth factors) and physical (e.g. cyclic mechanical loading) stimuli supporting tissue formation in vitro and in situA variety of synthetic biodegradable polymers has been investigated as TE scaffold materials, though the main disadvantage of these materials is their lack of functional groups In particular, poly-glycolic acid (PGA), poly-lactic acid (PLA), poly-hydroxy alkanoate (PHA), poly -caprolactone (PCL) and their deriving copolymers have generated substantial interest as scaffold materials for the in vitro TE of bone, cartilage, as well as cardiovascular tissues -lactide (PDLA) and LD racemic (PDLLA), respectively In 1998, Shinoka et al. reported surgical implantation of tissue engineered vascular grafts (TEVGs) in lambs, in which scaffolds were constructed from autologous cells seeded onto PGA grafts -lactic acid (PLLA) scaffolds for microvessels in mice -lactide and ε-caprolactone copolymer sponge for TEVGs in a canine inferior vena cava model -lactide and ε-caprolactone (PCLA/PGA or PCLA/PLA) are more elastic than the PGA scaffold However, in spite of their frequent use in biomedical research and therapeutic products, there is still a lack of systematic comparative analyses, such as qualitative and quantitative assays of tissue formation and biomechanics between different synthetic polymers. Therefore, the present study aims at a systematic, multimodal comparison of three frequently used polymers (PGA, PLA, PCL) integrated into a co-polymer solution with P4HB for the in vitro engineering of extracellular matrix under static as well as dynamic conditions. These data might allow for a specific selection of a certain polymer starter matrices aiming at specific tissue properties of bioengineered materials in vitro.Human umbilical cords (n = 3) were collected after full-term births with informed consent according to the cantonal ethics commission of Zurich, Switzerland [KEK-ZH-2009-0095] and processed for isolation of venous fibroblasts according to established protocols Isolated human cells (n = 3) were characterized using immunofluorescence staining for common myofibroblast markers. Therefore, cells were cultured on 3.5 cm2 cell culture dishes, fixed with 4% paraformaldehyde (Sigma-Aldrich, Switzerland), and incubated over night at 4 °C with the following primary antibodies: alpha smooth muscle actin (1A4, Abcam, United Kingdom), Vimentin (Vim 3B4, Abcam, United Kingdom), CD90 (EPR3133, Abcam, United Kingdom), CD31 (JC70A, Dako, USA), and Phalloidin (Life Technologie, Switzerland). The following secondary antibodies were used: anti mouse Alexa Flour 488 (Invitrogen, USA) and anti rabbit Alexa Flour 488 (Invitrogen, USA) and Dapi (Sigma-Aldrich, Switzerland). Cells were analyzed with a DM6000B fluorescence microscope (Leica, Germany). Image processing was performed using the Leica software (Leica, Germany).Cellular proliferation was assessed by determining the number of total cells based on the absorbance of crystal violet when cultured on a 24-well plate for up to 7 days. In brief, every day cells were fixed with methanol (Sigma-Aldrich, Switzerland) for 10 min and stained with 0.1% crystal violet (Artechemis, Switzerland) for 5 min. The 24-well plates were washed and air-dried. Cells were solubilized with 2% Na-deoxycholat (Sigma-Aldrich, Switzerland) while being heated at 60 °C for 10 min. The absorbance was analyzed at 550 nm using a standard ELISA reader Synergy HT (Bio TEK, USA). To obtain quantitative information a standard curve with serial dilutions was performed.Samples were mounted on electron imagining stubs using carbon tape and subsequently sputter coated in 5 nm of Pt/Pd (Quorum Technologies, EMS 300TD, USA) to reduce fiber degradation during imaging. A field emitting electron microscope was used to image samples at 15 kV power (Zeiss, FESEM Ultra Plus) for clarity. For each sample, four regions of interest (ROI) measuring 1000 × 800 um were imaged from which five fibers per ROI were measured using Image J software (NIH, v1.48s, line tool) to determine the average fiber diameter of an ROI. For scaffold porosity, an additional four ROIs measuring 3000 × 2250 um were imaged. Each porosity ROI image was then automatically thresholded in Image J and porosity was defined as the percent area that was non-fiber (ie empty/porous space).Patches were fabricated from non-woven polyglycolic acid (PGA) meshes (thickness 1.0 mm; specific gravity 70 mg/cm3; Cellon, Luxembourg) and coated with either 1% poly-4-hydroxybutyrate (P4HB; TEPHA, Inc., USA) or 1% Poly(-lactide) (PLA, Carbion, USA) or 1% polycaprolactone (PCL, Carbion, USA) by dipping into a tetrahydrofuran solution (Sigma-Aldrich, Switzerland). After solvent evaporation and vacuum drying overnight, the scaffolds were placed into a 70% EtOH (Sigma-Aldrich, Switzerland) for 30 min to obtain sterility, followed by two washing cycles with PBS (Sigma-Aldrich, Switzerland). Thereafter, scaffolds were pre-incubated in DMEM culture medium previously described for 12–24 h to facilitate cell attachment.Human fibroblasts (n = 3) were seeded onto scaffolds using a density of 1.5*106 |
cells/cm2. Therefore, fibrinogen (Sigma-Aldrich, Switzerland) (10 mg/mL of active protein) and thrombin (Sigma-Aldrich, Switzerland) were prepared, used and titrated to an optimal clotting time of approximately 30 s by adapting the concentration of fibrinogen. The cells were resuspended in a fibrinogen-thrombin co-solution and subsequently seeded onto the sterile scaffolds. After static incubation of seeded constructs in DMEM (10% fetal bovine serum; penicillin/streptomycin and 0.9 mM of -ascorbic acid-2-phosphate (Sigma-Aldrich, Switzerland)) for 7 days, they were kept either under static conditions or placed onto a shaker for additional mechanical stimulation via shear stress. The constructs were harvested after 21 days of culture and processed immediately for subsequent analyses.For immunohistochemical analysis of TE patches (n = 3 per group), sections with 5 μm thickness derived from blocks of formalin-fixed, paraffin-embedded tissue were mounted on glass slides (SuperFrost Plus, Menzel Gläser,Germany), deparaffinized, rehydrated and stained with hematoxylin and eosin (H&E) or Masson Trichrome using standard histological techniques. All sections were analyzed using a Mirax Midi BF slide scanner (Zeiss, Germany) and processed using MIRAX viewer (Zeiss, Germany).TE patches (n = 6 per group) were minced, lyophilized, and analyzed using biochemical assays for total deoxyribonucleic acid (DNA) content as an indicator for cell number, hydroxyproline (HYP) content as an indicator for collagen, as well as for glycosaminoglycan (GAG) content. All TE patches were digested in papain (Sigma-Aldrich, Switzerland) solution (300 μg/mL in PBS with 5 mM EDTA (Sigma-Aldrich, Switzerland)) and 5 mM cysteine (Sigma-Aldrich, Switzerland), at 65 °C for 16 h. For measuring the cellularity of the constructs, the DNA amount was quantified according to manufacturer’s protocol (Life Technologies, Switzerland, No. P11496). The GAG content was determined using a modified version of the protocol described by Ref. After 0 (only for the unseeded group) and 21 days of culture, the mechanical properties of the TE constructs (n = 4 per group) were assessed using a uniaxial tensile tester (Instron 5864, Boston, MA, USA) equipped with a 100-N load cell. For comparison, native tissues (cartilage, skin and vein) were harvested from sheep post mortem provided by the local slaughterhouse Zurich/Hinwil, Switzerland (n = 4). The crosshead speed was set to correspond to an initial strain rate of 7 mm/min and the tester operated at 5 bars of air pressure. Patches had a cross-sectional area of 14 mm × 4 mm × 1 mm (length × width × thickness) and were fixed with hydraulic clamps. Stress–strain curves were obtained and Young’s modulus was determined as the slope of the curve at a strain of 10%, as a measure for tissue stiffness.Quantitative data are presented as mean ± standard deviation. For statistical comparison of the proliferation rate of the three different cell lines a one-way ANOVA was performed and p-values < 0.05 were considered statistically significant. Surface morphology measurements were statistically analyzed by non-parametric Mann-Whitney-U test and p-values < 0.05 (corrected post hoc according to Bonferroni) were considered statistically significant. In addition, quantitative tissue analysis and biomechanics were statistically evaluated by an unpaired students-t-test and p-values p < 0.05 (corrected post hoc according to Bonferroni) were considered statistically significant. KS normality test was used to confirm normal distribution of the dataset (p > 0.05). All statistical analyses were performed using the GraphPad Prism 5 software (GraphPad Software Inc., USA).Immunofluorescence performed on fibroblasts derived from three different patients revealed that all cell types displayed similar immunophenotypic patterns. Isolated human fibroblasts expressed myogenic markers, such as alpha smooth muscle actin and vimentin, and common fibroblast marker CD90 (In contrast, the cells were negative for the endothelial cell surface marker CD31 excluding non-fibroblastic contamination during cell isolation procedures. In the proliferation analysis based on crystal violet staining (b), no significant differences in proliferation parameters were detected between the three fibroblast lines when considering cell numbers over 7 days (p < 0.05). These findings exclude potential significant inter-individual proliferation differences.Microstructural analysis using scanning electron microscopy (SEM) was used to analyze the fiber size and porosity of unseeded polymers before and after coating (a and f) was less porous in comparison to the hybrid polymers PGA-P4HB (d and i). Quantitative measurements of the porosity confirmed these differences (j). PGA-PCL scaffolds were significantly less porous than PGA-P4HB (p < 0.05) or PGA-PLA (p < 0.05) scaffolds. PGA-P4HB and PGA-PLA scaffolds showed a similar porosity with no significant difference (p = 0.69). Uncoated PGA mesh was significant more porous in comparison to PGA-P4HB (p < 0.05), PGA-PLA (p < 0.05), and PGA-PCL (p < 0.05). The fiber diameter was uniform among all biomaterials with no statistically significant differences between different hybrid polymer groups or uncoated PGA (f–i) display the distribution of the coating compared to PGA scaffold only. The different hybrid polymer present a similar distribution of the coating. In general, there was more coating visible on the outer scaffold regions, while in the central part of the scaffold less was detected.Microstructural features of human fibroblast-derived TE patches were analyzed by histological staining procedures (H&E staining demonstrated formation of extracellular matrix (ECM) in vitro with high cellularity and layered tissue on the outer scaffold regions, while in the central part of the scaffold low cellularity and no significant formation of ECM were present. In order to investigate the deposition of collagen fibers Masson Trichom staining was used. In general, TE patches under dynamic conditions (, right column) revealed more tissue formation and ECM deposition compared to static conditions.Importantly, all three cell lines exhibited comparable tissue formation for respective hybrid polymer conditions excluding a potential bias due to inter-individual differences. PGA-PCL-based patches showed for both culture conditions (dynamic and static) less tissue formation and high quantities of scaffold remnants in comparison to the PGA-P4HB or PGA-PLA. In order to confirm these findings polarization microscopy was performed to further visualize different polymer components (The starter matrices showed no major remodeling in the central part of the constructs in static as well as dynamic conditions given the lack of tissue formation in this area of the constructs. PGA fibers were visible as elongated ellipses (, high magnification), whereas the webbings between PGA fibers represented remnants of the coating (, low magnification). In dynamic conditions the biomaterial was more degraded (d–f) when compared to the static cultures (a–c). In particular, the PGA-PCL starter matrix (b and e) showed strong preservation of the polymer components compared to PGA-P4HB (The composition of the ECM of the human fibroblast-derived TE constructs was biochemically analyzed using assays for HYP, GAG, and the cell number (DNA) (The expression level of DNA, GAG, and HYP is for all 3 coatings higher under dynamic conditions than under static conditions. Analyses were performed after three weeks of static or dynamic culture. In general, no significant differences were detected between the three different cell lines relating to expression of HYP, GAG and DNA for respective coatings under static or dynamic conditions, indicating no inter-individual differences. In total, six TE patches per cell line and per coating condition were analyzed. PGA-P4HB showed a significantly higher expression of DNA, GAG, and HYP in comparison to PGA-PLA (p < 0.05) or PGA-PCL (p < 0.05) under static conditions suggesting a more rapid formation of ECM in vitro. Moreover, PGA-PLA exhibited a significantly higher expression of DNA and HYP than PGA-PCL (p < 0.05) under static conditions. Dynamically cultured PGA-PLA (p < 0.05) and PGA-P4HB (p < 0.05) patches expressed a significantly higher amount of DNA, GAG and HYP than PGA-PCL patches. PGA-P4HB (p < 0.05) also displayed a significantly higher DNA and HYP expression than PGA-PLA. In general, the expression levels of DNA, GAG and HYP were higher for all coatings under dynamic conditions compared to statically cultured patches.The material properties of the different TE patches used in this study were determined via uniaxial tensile tests in comparison to native ovine tissue, such as cartilage, skin and vein (). Stress–strain curves were obtained and Young’s modulus was determined as the slope of the curve at a strain of 10%, as a measure for tissue stiffness. Contribution of tissue formation to the mechanical properties was observed in all TE patches, given a higher elasticity with culture time in comparison to unseeded control. Due to the rapid loss of mechanical integrity of the scaffold, biomechanical tests on the TE patches under dynamic conditions over time could not be performed. Overall, PGA-PLA and PGA-P4HB TE patches show similar biomechanical properties. Both conditions display tensile stress of about 0.02 MPa and strain at maximal stress of about 20%. Tensile moduli of both 0.04 MPa and 0.08 MPa were obtained, which were not significantly different (p = 0.1479). In case of PGA-PCL, tensile stress was 0.54 MPa, tensile strain was 8%, and having a Young’s modulus of 4 MPa respectively. Generally, PGA-PCL showed a significantly higher Young‘s modulus, tensile strength and lower strain at maximal stress compared to PGA-PLA (p < 0.05) or PGA-P4HB (p < 0.05). For a better interpretation of the obtained results, also native ovine tissue were analyzed biomechanically. For cartilage, Young’s modulus was about 35 MPa, tensile strength was 12 MPa, and strain at maximal stress was 32.5%. In addition, skin had a Young’s modulus of 0.005 MPa, tensile stress of 14.5 MPa and tensile strain of 160%. Similar results were found for the vein with a Young’s of 0.0054 MPa, a tensile stress of 2 MPa and tensile strain of 185%.The tissue formation produced by implanted cells is highly influenced by the scaffold onto which they are seeded. Different types of biodegradable polymers as a scaffold have been investigated for tissue regeneration, such as PGA, PLA, P4HB and PCL So far, most biomaterials do not completely mimic physiological microenvironment and can therefore not enable native like cellular interaction and behavior For this reason, we performed SEM to analyze the ultra-structure of the unseeded scaffold. SEM confirmed the uniform fiber diameters of the coated PGA matrix. In contrast, PGA-PCL scaffolds were significantly less porous than PGA-P4HB or PGA-PLA scaffolds. PGA-P4HB and PGA-PLA scaffolds showed a similar porosity. These findings already suggested a potential improved cell infiltration and consequent tissue formation for PGA-P4HB and PGA-PLA in comparison to PGA-PCL. For example, porosity of the scaffold plays an important role in bone and cartilage regeneration Hence, microstructural features of human fibroblast-derived TE patches were analyzed by histological stainings as well as polarization microscopy. In general, tissue engineered patches under dynamic conditions represented a more extensive tissue formation and ECM deposition. Tang et al. also showed an enhanced cell proliferation under dynamic three-dimensional (3D) culture compared with conventional static two-dimensional (2D) and 3D cell culture conditions In general, dynamic conditions enhanced the degradation of biomaterial in comparison to static conditions. In particular, less PGA fibers were detectable after 3 weeks of culture in comparison to the webbings between the PGA fibers, especially PGA-PCL showed particularly strong preservation of the polymer components. Different studies have proven that PGA degrades faster than P4HB, PLA and PCL Importantly, a balance between the rate of scaffold degradation and tissue formation is crucial for maintaining mechanical integrity of the replaced tissues Biodegradable synthetic polymers are an interesting raw material for scaffold fabrication and have been intensively investigated for TE. As the scaffold plays a crucial role in the successful design of TE constructs, the choice of material directly influences the outcome. Our study may allow for a specific selection of a certain polymer starter matrices aiming at specific tissue properties of bioengineered materials in vitro. In general, we showed that PGA-P4HB coating display better tissue formation and a significant higher expression level of DNA, GAG and HYP in comparison to PGA-PLA and PGA-PCL. However, PGA-PCL is under biomechanical conditions more robust than PGA-P4HB and PGA-PLA.Future studies are required to evaluate, which combination under which conditions allow for the best tissue formation and native-like biomechanical properties.The authors declare no competing or conflicting financial interests.Some structural effects of plastic deformation on tungsten heavy metal alloysTungsten-based heavy metal alloys containing 90–97% W are two-phase composites combining high density, high strength and relatively high ductility. W content and manufacturing parameters have a strong influence on the deformation and fracture behavior of the alloys. Specimens with different content of W were prepared. The microstructure was studied after successive stages of plastic deformation, allowing the delineation of the weak regions of importance as fracture starting points. It was confirmed that the material plasticity increases substantially with decreasing tungsten content and that the deformation capability is determined by the condition of the W–W and W–matrix zone interfaces which is different at the compression and tension modes of deformation. A correlation between microstructure and mechanical properties was found and an explanation for the improved plasticity with lower tungsten content is given.Tungsten heavy alloys are a group of tungsten based materials with additions of Ni and other elements such as Cu, Fe, Co and Cr, and are produced by powder metallurgical methods. The applications of these materials include balance weights, kinetic energy penetrators, radiation shields, chatter-free boring bars and various sporting goods. The alloys are two-phase materials consisting of nearly pure tungsten grains embedded in a ductile FCC matrix. Tungsten heavy alloys are produced by a liquid phase sintering process. During the sintering, as a result of a solution-precipitation process, the fine tungsten particles of several microns in diameter transform into nearly pure spherical tungsten grains, typically 20–50 microns in diameter. WNiFe alloys differ from many other sintered alloys due to the unique combination of high density, high strength and plasticity, their ability to withstand heavy plastic deformation and the capability to improve their mechanical properties by strain hardening.The mechanical properties of the WNiFe alloys are so dependent on the technological conditions of their fabrication that until recently their manufacture was considered to be more an art than a technology. Subsequently, over the course of the past 20 years a number of works appeared which have widened our understanding of this class of materials The object of this paper is to clarify the correlation between the mechanical properties and microstructure of commercial liquid-phase sintered tungsten-based alloys with 90, 93 and 95 wt.% of tungsten. It is important to reveal the weak points of the structure by means of the observation of initiation and development of different modes of fracture in heavy metals with different tungsten contents with emphasis upon the difference between the tension and compression modes of deformation.Compression and tensile test specimens were prepared by pressing powder mixes containing 90, 93 and 95% of tungsten, respectively, and the balance Ni+Fe (ratio 7:3), and by subsequent sintering under reducing atmosphere. Since sintering temperature is a function of the tungsten content of the alloy, each composition was sintered under its own optimal sintering conditions. Before testing the specimens were annealed under an inert gas atmosphere at a temperature about 25% under the sintering temperature, in order to reduce the content of the absorbed hydrogen. Mechanical tests of pressed and sintered specimens were performed on a 10-ton MTS machine. The mechanical tests of the cold deformed alloys containing 90, 93 and 95% of tungsten were performed as well.A metallographic study of the alloys containing 90, 93 and 95% by wt. of tungsten was undertaken. To quantify their structure, the determination of contiguity was performed, where contiguity is defined as the relative interface area of grain-to-grain contact versus the total interface area in the liquid sintered alloy. Contiguity may be evaluated metallographically by measuring the length of phase boundaries per unit area of the micrograph. The equation for contiguity is:where Lww=length of W–W boundaries and Lwm=length of W–matrix boundaries.Tensile specimens were prepared as to MPIF Standard 10, and specimens for the metallographical observations of compression tests were prepared in prismatic (5×6×8 mm) form. Cylindrical specimens of 8 mm diameter and of 16 mm height for observation of fracture under compression were prepared as well. Some of the tensile and compression specimens were polished in the region of the expected deformation and a grid of diamond indenture marks was applied as has been previously described elsewhere Results of tensile tests for the three alloys in sintered and cold deformed conditions are presented in Typical microstructures of sintered and cold deformed alloy containing 93% by weight tungsten are presented in (a,b). The results of contiguity versus tungsten content for alloys containing 90, 93 and 95% W are shown in . The 90% W alloy had a large scatter in contiguity (between 0.2 and 0.4), possibly due to the presence of a large amount of the matrix phase and the tendency of tungsten grains to form clusters, separated by diluted areas. There are a number of additional reasons for the discrepancy between our results and those of the other investigators, i.e. the amount of the matrix phase may be different in different alloys. The method for definition of width of the interface boundary is quite arbitrary and may affect the results.Three stages were detected in fracture development by tension. In the first stage of deformation the opening of cracks at W–W contact areas is revealed (see ). The matrix phase absorbs all the deformation and precludes the crack propagation. The matrix absorbs the deformation up to a limit, which is about 10% of the elongation. During the second stage the plastic deformation is transferred from the open areas of the cracks through the matrix to the nearest tungsten grains. On the third stage of tension catastrophic failure of the specimen occurs as the result of the contribution of tungsten grain cleavage (see ). The same process is observed on specimens of 90 and 95% W the only difference being the initial numerical values of each stage.The behavior of the 90 and 95% W alloys under compression is presented in the micrographs shown in (a, b). The complex stress condition leads to a multitude of sliding plane directions. It may be seen that failure under compression begins at higher deformations. In contrast to the tension behavior, the grain to grain contact area separation was almost undetectable.The ability to withstand high compression deformation without failure allows the achievement of highly deformed material, usually by forging.The 90–95% W alloys show good dynamic properties. It may be seen from fractograms of the blow tested specimens. Two kinds of specimens of 90% W alloy were impact tested: sintered, and cold deformed. Two fracture surfaces resulting from a slow blow test at 5 m s−1 velocity are presented in . The fracture after compression deformation is presented on As may be seen from the results presented in this work, the tungsten content, among other factors, controls the fracture behavior of the tungsten alloys discussed in this work and correlates well with structural differences. The sintered alloys (see ) are similar in yield and tensile strength, but differ in their plasticity, as may be explained by the analysis of the tensile diagrams. The final segment of the load/strain curve of the 95% W alloy is much shorter than the one of the 90% W alloy. This can be explained by examination of the alloys’ contiguity () as well as crack initiation and development under tensile loading (). The three stages of morphological changes that are in agreement with the tensile diagrams are: (1) separation of the contacting grains of tungsten, which occurred as a result of plastic flow of the adjacent matrix phase at the initiation of the deformation by tension (), (2) creating slip bands and cleavage initiating at the adjacent tungsten grain because of subsequent deformation conducted through the strain hardened matrix phase, and (3) catastrophic failure of the specimen () due to the numerous cleavages of tungsten grains.All three alloys show higher plasticity under compression loading. The multiplane sliding of tungsten grains, their moving about one another and the matrix deformation provide a more complicated picture of the process, The separation of contact areas of tungsten grains and crack opening does not play the leading role in such a mode of deformation (see the morphology of the fracture on ). Deformation>40% is possible without cleavage of tungsten grains (see such a fracture views are presented for sintered and cold deformed 90% W alloys. The increased fraction of cleaved tungsten grains on the cold deformed specimen surface (b) as compared to sintered (a) must be noted. It correlates with the increasing role of strain hardened matrix phase in cleavage initiation of tungsten grains.Morphological studies have shown that failure under tension starts by separation of W–W interface areas and develops by producing cleaved tungsten grains after strain hardening the matrix phase. Failure under compression occurs after deeper deformation of the tungsten grains and the matrix than in the case of tension tests. The compression mode of fracture principally differs from the tension mode by the almost complete absence of separated W-W grain contact areas. In the absence of porosity, inclusions and detrimental impurities the main reason for initiation of fracture is multiple cleavage of tungsten grains. The plasticity of the alloy improves with increasing matrix phase between the grains and uniformity in its distribution. In the case of non-uniform distribution of the matrix phase and the presence of clusters of tungsten grains a consequently low plasticity may appear even in 90% W alloys.Finite element analysis of briquetting of iron ore finesBriquetting is a continuous compaction process to transform loose powders into solid briquettes. The density and strength of formed briquettes vary significantly in the process, affecting the quality of products. This work presented a numerical modelling of briquetting based on Finite Element Method (FEM), focusing on the evolutions of briquette structure and stress. The mechanical behaviour of powders was characterised by the density independent Drucker-Prager Cap (DPC) model. The parameters in the DPC model were determined by conducting experimental die compaction on iron ore fines. The stress distributions inside the briquettes at the maximum compression and ejection stages were analysed. The relative density, Von Mises stress and hydrostatic pressure showed clear declines from the top to the bottom. The effects of powder-wall friction and feeding pressure on briquetting were studied. The average relative density and power draw increased almost linearly with increasing feeding pressure. However, a nonlinear trend was observed with increasing friction. The results suggested that an optimal briquetting process could be achieved by selecting proper boundary conditions.Iron ore fines (size less than 6 mm) are created as a result of mining, crushing and processing large ore particles and they may stand for up to 50% of the total ore mined []. Iron ore fines need to be enlarged for better handling and transportation but also for increased permeability in the blast furnace.Briquetting is a continuous compaction process to consolidate powders into a block or briquette []. In briquetting, ore fines are drawn to two counter-rotating rolls and densified by high pressure from the rolls []. Different from roll compaction, there are a number of pockets on the roll surfaces with defined dimensions and sizes to produce briquettes with appropriate shapes and sizes []. Comparing to conventional sintering and pelletizing, briquetting is a cold bonding process and consequently less capital intensive and polluted than sintering, and it does not need milling materials to the size required for pelletizing.While briquetting is widely used in industries such as biomass, chemical, pharmaceutical and food industries, only limited research on briquetting has been reported [] investigated the effects of moisture content and operation condition on the briquetting of Hematite-Goethite iron ore fines. They evaluated that the feed moisture content was the most important briquetting parameter. Gannon et al. [] reported a patent on producing of iron ore briquettes that can be used in a blast furnace. Taulbee et al. [] evaluated the effects of binder and briquetting parameters for coal fines and sawdust. Their study showed that particle size and type had the greatest impact on briquettes properties while moisture content and briquetting force had minimum effects.Briquetting can be treated as a type of roll compaction which has been investigated extensively either by physical experiments [] examined the influence of the lubrication on the roll compaction of MCC powders. They showed that the peak stress, density and nip angle increased with roll friction. Inghelbrecht et al. [] found that roll pressure was the most important parameter affecting the strength of roll compacts followed by roll speed. It was observed that the mass throughput increased linearly with roll speed [] carried out a roll compaction of MCC powders and stated that the pressure-gap relation could be predicted by Johanson theory [To understand the evolutions of internal structure and stress of compacts, Finite Element Method (FEM) has been utilized to model roller compaction [] developed a 2D and a 3D FEM model with the mechanical behaviour of powders described by the Drucker-Prager cap (DPC) model. Based on the model, the effects of feed stress, roll friction and side seal friction on roll force, nip angle and relative density of the compacted powder were investigated. The simulation results were comparable with experimental trends. Later, Michrafy et al. [] claimed the parameters in the DPC model should be density dependent in order to obtain accurate results. They also observed that different feed condition has a strong effect on the homogeneity of formed ribbons. Comparing to the 1D Johanson model, FEM results were more comparable to experimental measurement as the velocity gradient was considered in FEM []. Muliadi et al. also conducted detailed comparisons between FEM results with experimental measurements []. The density-dependent stress–strain constitutive parameters to describe the powder mechanical behaviour were all based on the experiments. More recently, Mazor et al. [] conducted experimental and FEM study of the effect of sealing plates on the stress and density distribution of ribbons.Briquetting is more complex than roll compaction due to the complexity of briquetting (e.g. irregular boundaries), and the pressures acting on briquettes are oscillatory in nature. So, FEM modelling of this process is more challenging. The current study aims to develop a 2D FE model to simulate briquetting of iron ore fines. This allows us to test its feasibility, examine the accuracy of the parameters in the model and investigate the response of briquettes in a more efficient way. Physical experiments are conducted to determine the parameters in the FEM model. The stress-strain, pressure and briquette density at different stages are analysed. Finally, the effects of wall friction and feeding pressure on briquettes are examined.In FEM, a powder compact is treated as a continuous elastic-plastic porous material. Both elastic dεije and inelastic dεiji strain increments contribute to the total strain increment [where E and ν are Young's Modulus and Poisson ratio respectively, dσij is the elastic stress increment tensor and δij is the Kronecker delta.The plastic deformation of the compact is characterised by the Drucker-Prager Cap (DPC) plasticity model [, the DPC model is defined by three surfaces in the hydrostatic pressure - Mises Stress (p-q) plane []: a shear failure yield surface (Fs) at low hydrostatic pressure, a cap surface (Fc) at high pressure and a smooth transition yield surface (Ft) from Fc to Fs [The linear shear yield surface describes the dependence of the shear strength on the confining pressure and the compact is treated as a perfectly plastic body with no hardening or softening, given bywhere d is the inter-particle cohesion and β is the internal friction angle. The hydrostatic pressure stress p and equivalent Mises stress q are given by p=13σ1+σ2+σ3, and q2=16σ1−σ22+σ2−σ32+σ3−σ12, where σ1, σ2 and σ3 are the principal stresses. For the uniaxial compaction, σ1 = σz and σ2 = σ3 = σx, where, σx and σz are the stresses in the X and Z axis. So p=13σz+2σx and q=13∣σz−σx∣.The cap surface describes the dilation/densification behaviour of the compact at high pressure, which expands or contracts with the inelastic volumetric strain decreasing or increasing. It consists of an elliptical cap segment with a constant eccentricity, given bywhere R is the cap eccentricity which expands or contracts with the change of volumetric strain and α is a small value (between 0.01 and 0.05). Pa is the evolution parameter which can be obtained from the maximum hydrostatic pressure stress of the cap Pb.Ftpq=p−Pa2+q−1−αcosβd+Patabβ2−αd+Patanβ=0The determination of the parameters such as elastic modulus (E) and Poisson's ratio (ν), cohesion (d), internal friction angle (β), cap eccentricity (R) and hydrostatic yield stress (Pb) were calibrated by conducting compaction experiments as described in In the study, a 2D FEM model was developed using a commercial software package Abaqus/Explicit [] to model the dynamic briquetting process. shows the briquetting system simulated in the study. The true density of iron ore fines (mainly goethite and hematite) was 4314 kg/m3, and the initial bulk density of the compact was 1952 kg/m3, giving the initial relative density of the powder bed 0.45. The roll speed was 10 rpm and the feeding pressure was 2 MPa. The selections of these values were based on previous studies [b shows the 4-node plane strain element (CPE4R) mesh for the study. As the feeding region is comparable with the compaction region, the default Lagrangian mesh domain was assigned to the region which was occupied by iron ore fines. In the process, the nodes moved as the material flowed, and the meshes were adapted to be tangent to the roller boundary surface []. Mesh independence was conducted in the study by varying the size and number of mesh. Further reducing the current mesh size (1 mm) shows no significant effect. The effects of gravity and interstitial air were neglected. shows the parameters used in the simulations.The parameters in the DPC model were calibrated based on experimental compaction tests using an Instron 5566 test machine (), including single punch die compaction, unconfined axial compression and diametrical compression. In the experiments, iron ore powders with the size 25–75 μm were dried in an oven for 12 h, then were mixed with 5% water. In the experiments, different amounts of water were tested and the compacts mixed with 5% of water had the largest strength which was comparable with previous work []. Lubricant was only applied on the die wall to reduce the friction between the iron ore particles and the die wall. The powders were then compacted in the die with 24.5 MPa loading (a). After the die compaction, the sample was ejected from the die, which was then used for the unconfined uniaxial ( shows the experimental results of the tests. a is the compaction curve of die compaction, which was used to determine the elastic parameters, such as modulus of elasticity (E) and Poisson's ratio, and hardening function. The peak values in b and c were used to calculate the compressive (σc) and tensile (σt) strengths of the compact and to determine the parameters in DPC model. The average axial breaking force is 40.48 N with a standard deviation 4.04, and the average diametrical breaking force is 1.43 N with standard deviation 0.19.The experimental results were used to determine the parameters in the DPC model. However, the radial wall stress was not measured due to the limitation of the facilities. Therefore, some of the parameters were determined through trial-and-error. A number of simulations were conducted with different values in order to have to the best match of the experimental measurements. As the change of density from the initial state to the final state was relatively small compared to the die and roll compactions, the parameters were independent of compact density.Elastic Parameters (E and ν): Poisson's ratio was set to 0.22 based on trial-and-error and the value was comparable with the previous studies []. The Young's modulus was determined from the slope of the line AB in the unloading curve of the die compaction, given by [From the experiments, the Young's modulus was 1052 MPa.Plastic Parameters (β, d, R and α): R is a material parameter controlling the shape of the cap. Previous studies have shown R is in the range of 0.1–1 and α 0.01–0.05 []. In this study, the cap parameter R was set to 0.629 based on the trial-and-error test, and α was arbitrarily set to 0.03. Cohesion d and internal friction angle β were determined by [σc and σt are the compressive and tensile strengths of the compact, respectively, as determined from b and c. Cohesion d and friction angle β were 5.02 MPa and 68.22°, respectively.Hardening function and friction coefficient: In the DPC model, Pa and Pb are the onset and maximum hydrostatic compression yield stresses. In the model, Pb can be obtained by,where Pa was obtained from the compaction curve, given by,, Pa and Pb were obtained at different densities. shows the hardening function between Pb and volumetric plastic strain Evolin=lnρρ0, where ρ0 and ρ are the initial and current relative density of the compact. The hardening function was fitted bywhere C1 and C2 are the fitting parameters.The coefficient of friction between the iron ore fines and the die surface was set to 0.2 to match the compact response in the experiments.With the parameter values calibrated from the experiments, the simulation was able to re-produce the compaction curve comparable to the measurement, as shown in . In the experiments, 3KN (~24.5 MPa) force was applied to compress iron ore fine into a compact with a relative density of 0.86, which is a typical value for briquettes. In the following section, the model will be used to analyse the briquetting behaviour of iron ore fines.After the parameters in the FEM model were calibrated and validated based on the die compaction experiments, the same set of parameters were applied to the briquetting process. While there has no experimental data on briquetting for model comparison, it is reasonable to assume the simulation results can reflect the real process as the same iron ore materials were used in both die compaction and briquetting. shows the variations of the total force and power draw on the rolls during the briquetting process. The force is the summation of all the forces acting horizontally on the two reference points. Six cycles are observed in a, corresponding to 6 briquettes formed. Except for the first cycle, other 5 cycles have a similar pattern with the maximum peak up to 1400 N/mm (assuming the depth is 1 mm) and the minimum force of 750 N/mm. It indicates that the process reaches a steady state after the first briquette. The power draws in b, calculated from the total torque acting on the rolls and the rotation speed [], shows a similar pattern. The maximum power draw in the process is about 175 W/mm. From the figure, two particular stages, A and B, can be selected, corresponding to the maximum compaction and ejection stages. In the following analysis, the properties of a briquette at two stages will be discussed. shows the distributions of relative density at two stages. The distributions at Stages A and B show a similar pattern, indicating the briquette structure experiences little change once the powders are compressed. Both stages show a higher density region at the upper part which gradually decreases from top to bottom. The results suggest that the lower part of the briquette is much looser than the upper part. The high density area decreases slightly at the ejection stage due to the elastic recovery of powders. In the simulation, the local density higher than 0.95 was mainly due to the small size of cells in the calculation. This does not affect the overall relative density. A previous study by Cunningham [b shows the density distributions through the centre line XY. Again the density distributions for Stages A and B are similar except at the shoulder region where the maximum density exists. shows the distributions of pressure and Von Mises stress at two stages. a shows that at stage A with maximum pressure, the pressure distribution exhibits a clear gradient from top to bottom. A similar pattern is also observed for Von Mises stress. However, the maximum Von Mises stress is at the neck region while the maximum pressure is near the centre. The inhomogeneity of the pressure and Von-Mises (as well as density) are due to the friction between the briquette and the roll, and internal friction. In addition, the individual contacts between particles also cause the distribution of stress inside the briquettes. At Stage B when the briquette is ejected from the rolls (b), both pressure and Von Mises stress decrease. shows the corresponding distributions at two stages. Pressure at stage A shows a wider distribution (a) whereas the pressure at stage B is smaller and more concentrated with a peak at 4 MPa. The Von Mises stress exhibits a similar trend (b). The change of the distributions indicates the reduced and more homogenous stresses at stage B comparing with those at stage A.As the particle flow is in the vertical direction and the pressure comes from the horizontal direction, the tensile and compressive stresses inside a briquette can be analysed from the two directions. shows the horizontal (S11) and vertical (S22) stresses at two stages. At Stage A when the powders experience the largest compression from the rolls, a shows that the horizontal stress is compressive (blue colour) at the upper part of the briquette and tensile (red) at the bottom. Both the maximum compressive and tensile stresses occur at the centre line. On the other hand, the vertical stress has the maximum compressive and tensile stresses at the upper part. This is due to the downward flow of the particles, causing the tensile stress at the neck region and compressive stress just below the neck. At stage B after the briquette is ejected from the rolls, a large amount of tensile stress residue still exist inside the briquette, particularly at the upper part (b). These residues can cause crack/fracture of briquettes in the downstream handling processes.Understanding where the powders experience plastic yielding in the process is important to predict where the crack/fracture of briquette is initiated. This was achieved in ABAQUS by activating the output variable ACTIVE YIELD, which provides equivalent plastic strains for shear failure surface as shown in . The red colour indicates where the material yieldes and the blue colour specifies that no plastic strain occurres []. It is noticed that the distribution of plastic strain begins from the boundary and propagates to the centre. While AC YIELD cannot be directly linked to the failure or crack of briquette, its pattern is very similar to the crack pattern observed in the experiments. So it may provide an implication about failure or cracks based on the output of plastic strain. A previous study [] has demonstrated that under this condition the compact will fracture into two parts along the central line without being capped. This indicate the briquette has a tendency to break into two parts vertically.The powder-wall friction plays a vital role in powder compaction as it leads to the variation of relative density, structural states inside the compact and influences the loading and unloading force histories []. Moreover, it is the main factor to pull particles into the rolls []. It therefore important to understand how friction affect the property of formed briquettes. compares briquette density and Von Mises Stress distributions in the briquette after it is ejected from the rolls. The density increases with increasing coefficient of friction between the particles and roll surfaces. With large friction, particle motion is obstructed at the surface, causing a higher density region at the upper part with a larger density gradient in the flow direction. A similar trend was also observed in roll compactions []. Similarly, a higher Von Mises stress region also concentrates at the neck position, which increases with increasing friction. With increasing friction, the Von Mises stress at the bottom part also increases. illustrates the mean relative density and power draw for the different coefficients of friction. a shows the mean density increases sharply till the coefficient of friction reaches 0.3 beyond which the increase becomes much slower. A similar trend can also be observed in power draw although the slowdown after 0.3 is less significant compared to density (b). It indicates that the briquette density is almost a constant after friction reach a certain level even the power required still increases. Therefore, choosing appropriate friction is essential to obtaining a more uniform briquette.Feed pressure is the most important factor in roll compaction and has an extensive effect on the strength of compacts [ shows the comparison of the relative density and Von Mises Stress distribution with different feed pressures. With increase of pressure from 1 MPa to 4 MPa, the density increases significantly at the top and bottom parts of the briquette. This is because more particles flow into the roll pockets with higher feed pressure. The Von Mises stress also increases with increasing pressure. However, there is no visible change to Von Mises stress in the middle part of the briquette. plots the mean relative density and mean power draw as a function of feed pressure. An increase of feed pressure results in adequate compaction which leads to stronger briquettes with higher relative densities. a shows that the average relative density rises almost linearly as feed pressure increases. b also illustrates a similar trend for the power draw of the briquetting process. This phenomenon was also reported by Dec et al. []. It indicates that the densification of powders inside the pocket proliferates with increasing pressure.The briquetting behaviour of iron ore fines was investigated using the Finite Element Method (FEM). The Drucker-Prager Cap (DPC) model was utilized and the parameters were determined by conducting physical experiments of die compaction, uniaxial compression and diametrical compression. The evolutions of briquette structure and stress were analysed. The effects of friction and feed pressure were examined. The main findings can be summarised as follows.The evolutions of the total forces and power draw in the briquetting process were obtained, showing oscillation patterns with the maximum force up to 1400 N/mm and the minimum force 750 N/mm.Relative density, Von Mises stress and pressure were higher at the upper region of the briquettes and gradually decreased along the flow direction. While the stress at the loading stage was compressive, the residual stress in the ejected briquetted were mainly tensile which can used to predict the fracture of briquettes. The plastic flow began at the boundary and propagated to the centre.The increasing friction showed a nonlinear increase in briquette density, von Mises stress and power draw. An extensive increase of structural states inside the pocket was also observed with increasing feed pressure.Our work can be help optimise the briquettes process of iron ore fines. In this work, a numerical model of briquetting process has been conducted to analyse the physical and mechanical properties of briquettes so that the optimal conditions of briquetting can be identified.Effect of temperature and humidity on the breakage behaviour of Aspirin and sucrose particlesThe effects of temperature and humidity on the breakage propensity of two organic materials, Aspirin and sucrose, were investigated. The breakage propensities of both materials were found to be insensitive to humidity at ambient temperature; however they both showed a change in their impact breakage extent as a function of temperature, with Aspirin showing a more pronounced trend as compared to sucrose. Using the breakage data as a function of temperature, a lumped parameter, representing hardness, H, and fracture toughness and having the form H/Kc2 according to the model of Ghadiri and Zhang [1], was evaluated as a function of temperature. The value of this parameter also showed an increase with temperature, indicating that the fracture toughness of Aspirin should decrease with an increase in temperature, considering the functional form of the parameter. In addition, its breakage propensity as a function of temperature was found to be well described by the Arrhenius equation from which the activation energy, − 19.04 J/mol can be explained as equivalent to the energy required to overcome plastic deformation and initiate fracture.The breakage of Aspirin, characterised by single particle impact tests, was found to increase with temperature. Additionally, the breakage propensity of Aspirin as a function of temperature was found to be well described by the Arrhenius equation. The activation energy, 19.04 J/mol, can be explained as equivalent to the energy required to overcome plastic deformation and initiate fracture.Size reduction of particulate solids by milling is one of the most important unit operations in the food, fine chemicals, and pharmaceutical sectors. In the pharmaceutical industry the interest in milling is not only focussed on producing drug particles in specified size distributions, but also on polymorphism, stability and amorphous content. The outcome of a milling process depends on the mill dynamics, environmental conditions and properties of the materials. For the latter, the relevant mechanical properties are hardness, Young's modulus, and fracture toughness Plastic deformation of crystalline materials occurs by the movement of dislocations which enable slip to occur. Plastic flow in crystalline materials is influenced by lattice structure, and the type of bonding present and lattice defects During bulk milling of particulate materials, a percentage of the input energy is dissipated as heat, resulting in an increase in the temperature inside the mill. This may in turn affect the mechanical properties and flow characteristics of the material being milled and consequently the quality of the milled product. Additionally, prolonged milling of particles could cause a lowering of their melting points; a situation which when coupled with the presence of high temperatures could result in agglomeration of the material, particularly those in the sub-micron sized range, inside the mill. Cryogenic milling may be used to counteract increased temperatures during milling, or to embrittle materials which normally fail in the ductile mode, however, it may not be effective for some organic materials because the response of materials to temperature may differ. Hence, the understanding of temperature effects on breakage behaviour is of extreme importance.Little work has been found in open literature on the effect of temperature and humidity on the breakage mechanisms of materials, and especially of single organic molecular crystals. This could partly be due to the difficulty and time consuming process of growing large enough crystals in which these effects can be observed. In addition, this class of materials has comparatively much lower melting points to metals and ceramics so that the temperature range at which temperature effects on slip and fracture can be observed is limited to only a few tens of degrees. In addition, the temperature effects of these materials might have associated effects of humidity to which they could be sensitive. Using a Vickers indenter, Duncan-Hewitt and Weatherly In this work, the effect of temperature on the single particle impact breakage behaviour of two materials, acetyl-salicylic acid and sucrose, has been investigated using the single particle impact test method described by Yüregir et al. Acetyl-salicylic acid (Aspirin) and sucrose were selected for testing as model materials as both materials are widely used in the pharmaceutical industry as active ingredient and excipient, respectively. The Aspirin used in this study is classified as grade Purum, Fluka with an assay of ≤ 99% obtained from Sigma Aldrich, UK. The sucrose used was of the table sugar variety, Silver Spoon brand, obtained from food shops. The samples were prepared by hand sieving using BS410 sieves (Endecotts Ltd., London, UK) to provide samples in a single sieve size range of 425–500 µm.Prior to testing the materials at different temperatures under ambient humidity conditions, the samples of sieve size range 425–500 µm are weighed to about 2 g and stored in air tight jars. These samples are then maintained at the test temperatures for at least 48 h. Higher temperatures are achieved by storing the samples in a temperature controlled oven while for sub-ambient temperatures the samples are stored in a temperature controlled freezer.To investigate the effect of humidity, saturated salt solutions are utilized to obtain a range of relative humidity conditions to study the effects of moisture on the single particle impact breakage behaviour. This method relies on the principle that the partial vapour pressure of water above a saturated salt solution in equilibrium with its surroundings is a constant at a particular temperature. Zero or extremely low humidity is achieved with the use of silica beads and calcium oxide powder acting as desiccants. The temperature of the laboratory ranges from 20 to 25 °C. To ensure a saturated solution, 50% more than the solubility weight of each salt is added to 100 ml of distilled water and left in the bottom of 22 cm diameter sealed glass desiccators for two days to equilibrate. The desiccators are then placed into an oven maintained at 25, 50 or 70 °C and the samples placed in the desiccators. The samples are assumed to be at equilibrium when the sample weight stays constant over a period of 48 h. For convenience and consistency, all samples are stored in the desiccators for 48 h. To monitor the relative humidity of the saturated salt solutions in these desiccators, the temperature/relative humidity sensor is inserted through the hole of the desiccator lid. This reading is taken after about 1 h, by which time the sensor is stabilized at the incubator temperature. Subsequently, the particle is introduced into the single particle impact device as described in the next section. To minimise temperature fluctuations of the feed material before impact tests, the samples are removed from stored temperature with the aid of a polystyrene holder also maintained at the same temperature.Impact testing is carried out using a test rig following the Yüregir et al. with C1 representing the combined physical and mechanical properties shows the results of the single impact tests performed on 425–500 µm sucrose and Aspirin for the four different humidity conditions at 25 °C.At very low impact velocities ∼ 1.5 and 10 m/s for Aspirin and sucrose respectively, very little or no breakage is observed for both materials. According to Vogel and Peukert also show little change (ranging between 0.0214 and 0.0237 for sucrose) over the humidity range tested, confirming that moisture does not have a significant effect on the breakage behaviour of sucrose and Aspirin at 25 °C. Similar results have been observed by impacting sucrose particles exposed to different moisture content levels at different temperatures.The results of the breakage propensities of sucrose and Aspirin as a function of temperature at ambient humidity are shown in , respectively. Both materials show a change in breakage propensity with temperature change.For both materials, no change in the breakage propensity can be observed as a function of humidity as shown in . While there is a change in the breakage propensity of sucrose as a function of temperature, the trend is not a clear one. As the temperature is increased from −20 °C to 25 °C to 70 °C, the breakage propensity increases and then decreases. The breakage propensity of Aspirin shows a clear trend as a function of temperature as given in ; the breakage propensity increases noticeably as temperature increases. In addition the data, fitted to the power of ∼ 2, shows good agreement with the Ghadiri and Zhang . For Aspirin, the tests were carried out at an additional temperature 50 °C, but no major difference was observed between the tests at 50 °C and 70 °C as shown in the C1 values in , hence the data for 50 °C are omitted from further analysis. The increase in the breakage propensity of Aspirin with increasing temperature is reflected in the values of C1/ρl which increases, corresponding to an increase in H/Kc2. However, the effect of temperature on hardness and fracture toughness cannot be deduced independently as the measurement of the fracture toughness for small particles at high strain rates is difficult. Therefore the combined mechanical properties responsible for the breakage can only be measured indirectly using single particle impact tests.From the limited published work in literature on the effect of temperature on hardness of organic materials, an increase in the temperature of sucrose and acetaminophen by Duncan-Hewitt and Weatherly While almost no literature has been found on the effect of temperature on the fracture toughness of molecular organic materials, some work has been carried out on measuring the micro-indentation hardness of ceramic materials. The micro-indentation fracture toughness measurements of aluminium oxide and silicon nitride carried out by Lee and Brun The above information suggests that an increase in testing temperature, as was carried in this study, should have the effect of reducing both the hardness and fracture toughness of Aspirin. However, comparing the values of C1/ρl which is proportional to H/Kc2 in the Ghadiri and Zhang shows that, according to the above trend, increasing the temperature increases the overall value of the group H/Kc2. A plausible reason for this could be that both the hardness and fracture toughness reduce with temperature but the effect of fracture toughness reduction is comparatively greater and this situation would have the overall effect of increasing the value of H/Kc2. A similar trend may also be observed if the hardness remains the same but the fracture toughness reduces. Moreover even if the hardness and fracture toughness both reduce by the same extent, it is expected that the reduction in the fracture toughness with an increase in temperature would have a more profound effect on the breakage propensity since the fracture toughness value in the denominator is squared. This is illustrated in . From the mechanical properties of Aspirin measured by nano-indentation (not shown here), an analysis was carried out, reducing the values of H and Kc (obtained from indentation tests) by 1% successively to find out which of these would have the greater effect on the overall breakage of the material. It is acknowledged that the H/Kc2 values measured using nano-indentation may not be similar to the expected values at higher strain rates during impact but they are used to give an indication.From the nano-indentation studies (not shown here), the propagation of cracks in Aspirin was observed to occur along cleavage planes, by the SEM images of the particles after single particle impact. The work of Iwasa and Bradt The observation of temperature on the breakage of Aspirin can also be analysed by considering the parameters, plastic contact time and impact force, used in the derivation of the Ghadiri and Zhang An increase in temperature would cause a decrease in hardness and therefore an increase of the plastic contact time, as described in Eq. where tp, ρ, l, and H, are plastic contact time, density, particle size, and hardness, respectively.An increase of the plastic contact time would cause a corresponding decrease in the impact force, F, defined in Eq. By substituting the impact velocity with impact force (defined above) into the Ghadiri and Zhang , increasing the temperature is expected to decrease the impact force. According to Eq. , this should cause a reduction (R⁎) in breakage at higher temperatures. Instead, an increase in breakage is observed when the temperature of the particles is increased. Therefore the value of the fracture toughness must decrease in order for this to happen.Based on the above analyses, it is concluded that the increase in breakage propensity of Aspirin with temperature is due to a reduction in both hardness and fracture toughness of the material.The variation of C1 with temperature for Aspirin is represented in the form of an Arrhenius equation, lnk=lnA+−EaR1T, as shown below:where C1 is the equivalent of a rate constant of chemical reaction, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant (8.314 J K−1 |
mol−1), and T is the temperature (K). The plot of ln C1 versus 1/T is shown in A good linear fit between ln C1 and 1/T is obtained indicated by the value of R2. This shows that the dependence of C1 is well represented by the Arrhenius equation; ln C1 is equivalent to the rate of change of the combined mechanical properties H/Kc2 and the value −19.04 J/mol (i.e. the product of the gas constant, R, and −2.29) is equivalent to the activation energy. Plastic deformation (the resistance to which is measured as hardness) occurs by the movement of dislocations and precedes fracture of semi-brittle materials. Hence it is possible that the activation energy is related to the energy required to move dislocations and initiate fracture in Aspirin. To establish a relationship on this line requires further work. SEM analyses of the product (not shown here) do not show any perceptible difference in the breakage morphology of this material at different temperatures.The breakage propensities of Aspirin and sucrose are insensitive to humidity. Conversely, both materials show a change in their impact breakage as a function of temperature. While the trend for sucrose is not a clear one, for Aspirin, its breakage propensity clearly increases with temperature. By evaluating the breakage data i.e. a lumped parameter, representing hardness, H, and fracture toughness and having the form H/Kc2 according to the model of Ghadiri and Zhang The findings of this work would be examined further by carrying out nano-indentation tests on single particles of both materials at different temperatures.The analysis of diagonal crack propagation in concrete beamsLongitudinally reinforced concrete beams without stirrups were examined. Shear span-to-depth radio (a/d) is the main parameter that affected their work. According to a/d differences of diagonal crack propagation were observed in tests. Numerical simulations confirmed the change of failure mechanism when a/d |
< 2.5.This paper deals with flexural concrete members reinforced longitudinally but without transverse reinforcement. The conducted experimental investigations have shown that beams without web reinforcement may fail without attaining their full flexural capacity and then shear governs their failure. In the paper, there are presented recent results of the author’s own experiments, which aimed at disclosing some aspects of the propagation of cracks in longitudinally reinforced concrete beams without stirrups. The experimental program has been designed to investigate the influence of the shear span-to-depth ratio on diagonal crack propagation and load carrying capacity of tested beams. The obtained test results were compared with numerical results made on the basis of Finite Element Method. In the performed numerical simulation the same longitudinally reinforced concrete beams as in the test were considered. During the numerical analysis, the special attention was paid on a tensile stress distribution and on changes of diagonal crack propagation in dependence of the shear span-to-depth ratio in calculated beams.A number of experimental and theoretical investigations, for example The influence of concrete properties on shear carrying capacity of concrete beams reinforced longitudinally was analyzed by Desai. In papers where: fc – characteristic compressive cylinder strength, Vult – ultimate shear force.A big research program concerning shear failure of reinforced concrete beams was performed in 1960s by Kani presents versus a/d for beams with different reinforcement ratios. Based on the obtained results Kani noticed that “… νu for heavily-reinforced, short beams was in the order of 15 times greater than for long beams with a low percentage of reinforcement, although the concrete strength remained constant.” According to Kani, the shear strength depends on the shear span-to-depth ratio a/d and reinforcement ratio ρ (see , the researchers observed that the shear strength of tested beams was primary depended on the shear span-to-depth ratio. They noticed two type of failure in tested beams. The first type was characterized by diagonal tension cracking and it appeared in tested beams of a/d |
> 2.5. The second type was by shear-compression for beams with a/d |
⩽ 2.5. Shuaib and Lue concluded that the amount of longitudinal reinforcement influenced the load level at which failure appeared but did not have an effect on the type of failure mode.On the basis of performed experimental research presented in professional literature the following conclusions can be drawn:The shear strength of concrete beams reinforced longitudinally but without transverse reinforcement depends on the shear span-to-depth ratio, reinforcement ratio, and concrete strength.The shear span-to-depth ratio, as it may be suspected, has also significant influence on the mode of shear failure.Other parameters such as reinforcement ratio and concrete strength have rather quantitative than qualitative effect on propagation of diagonal cracks.The question arises as how to explain the difference in failure mechanism in dependence of a/d. The author’s own experimental program has been performed to analyze the influence of the shear span-to-depth ratio on failure process and cracks propagation of concrete beams with longitudinal reinforcement and without stirrups.Four concrete beams were tested in a four-point bent test (beams S2, S3, S4 and S5). The external forces were applied symmetrically. Beams were 2.05 m long and the beams’ effective span during the test was constant, leff= 1.80 m, whereas the distance between external forces, c, was different in every beam. All beams had the rectangular cross section of the width b |
= 0.12 m, the total height h |
= 0.25 m, and the effective depth d |
= 0.22 m. The variable distinguished between beams was the shear span-to-depth ratio, a/d, from 2.3 to 3.4. The static scheme realized during the test is shown in and details of test specimens are given in The beams were made from the same grade of concrete and the maximum diameter of aggregate was 16 mm. Control specimens were cast and cured simultaneously with beams: cylinders 150 mm in diameter by 300 mm high to determine the compressive strength and the Young’s modulus and cylinders 160 mm in diameter by 160 mm high to determine the splitting tensile strength. They were tested soon after the beam test. The results obtained on the control specimens are given in . The axial tensile strength, fct, was estimated from the mean splitting tensile strength, fct,sp, according to CEB FIP MC 90 Two deformed steel bars with diameters of 18 mm were used as bottom longitudinal reinforcement in all tested beams. As the nominal area of single 18 mm bar is 254 mm2, so the total area of longitudinal reinforcement was As= 508 mm2 and it gave the ratio of reinforcement ρ |
= 1.8%. Mechanical properties of steel bars were measured during the direct tensile test on ten samples. The determined mean value of the yield stress was: fy= 453 MPa and the mean value of tensile strength was: ft= 698 MPa.All beams were tested to failure under symmetrical two-point top loading system. Monotonic loading was provided using a 6000 kN universal testing machine ZD600. Loading and instrumentation arrangements are shown in . Both surfaces of the tested beams were whitewashed to make the observation of crack development during testing easier. Crack widths were measured directly by using handheld microscopes on one side of every beam for all cracks but special care was made to measure diagonal cracks. The smallest division of the microscope was 0.05 mm. Microscope measurements were made at every interval of applied load at five levels marked on the beam’s site. Vertical deflections near the supports and in the mid span were measured by using dial test gauges. Horizontal deflections with the reference to the edge of the beam were measured to check the bond between concrete and reinforcement. For this purpose dial test gauges were installed on the ends of steel bars, which were put out of the member.The cracking shear force, Vcr, was assumed as the shear force that caused the first diagonal cracking. In all tested beams, concrete cracked at first in flexure at the bottom face. At larger loads, the shearing stress caused those cracks to change their orientation near mid-height of the section and became diagonal cracks. The ultimate shear force was taken as half the applied central load at failure read from the testing machine, Vult= |
0.5Pmax.The cracking and ultimate forces reached during the experiment, Vcr and Vult, and the calculated values of Mcr and Mult are given in , where Mcr is the cracking moment and Mult is the ultimate moment including the shear influence:The characteristic parameter for the flexure-shear interaction, assumed as the ratio Mult/Mfl, is also written in . Mfl is the moment capacity in pure flexure calculated as:where fy – the mean yield stress of the longitudinal reinforcement, As – the cross section of longitudinal reinforcement, z – the inner level arm.The ultimate shear capacity Vult was significantly higher for the beam S4 of a/d |
= 2.3, as compared with other beams of a/d |
⩾ 2.5 (see ). The biggest reduction of beams capacity caused by shear, Mult/Mfl , was obtained during the experiment at the shear span-to-depth ratio a/d |
= 2.5, what is visualized in Flexural cracks initiated in the mid span of all tested members at approximately P |
= 36 kN. When the load was increasing, new cracks started to appear and the existing cracks widened insignificantly. In three tested beams S5, S3, and S2 the failure process went in the similar way, as shear transfer along one diagonal crack, which ran only at one side of the beam from the applied force to the support. The failure crack developed from the flexural crack when the load was close to the maximum. These beams failed suddenly in shear, soon after the appearance of diagonal crack. In the beam S4, characterized by the smallest value of the shear span-to-depth ratio, the failure process went in a different way. Two flexural-shear cracks appeared when the load reached 50% of the maximum and they did not develop from the flexural cracks. As the load was further increasing, new cracks did not form but the already existing cracks widened. The main diagonal cracks formed nearly symmetrically at both opposite support zones of the beam S4. Those cracks were inclined at approximately 29° to the horizontal axis. From the stage of 2/3 of the maximum load up to the failure only the main diagonal cracks widened and one of them became the failure crack. Cracks patterns obtained in tested beams are shown in The results of cracks width measurements showed very similar and slow increase of crack widths in all beams until the force about 80 kN. For the beams S5, S3, and S2 with a/d |
= 2.5, 2.7, and 3.4 the maximum measured crack width before failure did not exceed 0.1 mm. For the beam S4 of a/d |
= 2.3, further increase of diagonal crack width was noticed for the applied force up from 80 kN to failure and the maximum crack width reached 0.7 mm.In presented experimental investigation, it has been found that in all tested beams the diagonal failure takes place. The obtained relative strength Mult/Mfl is always less than 100% and no full flexural capacity is attained. In relation to the values of the parameter a/d, the beams reach failure under a bending moment smaller than such beams can sustain without shear. All values of Mult range between 0.50 and 0.93 of Mfl. The lowest value of Mult, equal half of Mfl, is at a/d |
= 2.5.According to the experimental results, the shear strength of simply supported beams is significantly affected by the shear span-to-depth ratio a/d. The resistance mechanism starts to change at a/d less than 2.5. In the beam S4 with a/d |
= 2.3 the ultimate shear force was about two times greater from those of the beams with a/d |
= 2.5, 2.7, and 3.4, although all tested members were made from the same grade of concrete, were reinforced in the same way, and had the same dimensions. On the basis of the obtained results, it may be concluded that, for design analysis, beams should be divided on slender beams with a/d |
⩾ 4.1. and short or deep beams with a/d |
< 2.5.Taking into account the obtained patterns of cracks, it may be concluded that concrete tensile stress occurs both in the compression zone (above the neutral axis), where concrete is subjected to a multi axial state of stress, and in the tension zone by means of the aggregate interlock mechanism and dowel action. The tensile strain capacity of concrete being low, shear failure is generally brittle and, hence, more dangerous than a flexural failure in which the tensile strain capacity of the steel reinforcement causes ductile behavior.The obtained results show that, except for the local failures such as anchorage failure and bearing failure at supports and loading points, the shear failure of the beam is caused by diagonal crack, although the failure mechanism varies according to a/d. For slender beams with a/d |
> 2.5, an inclined tensile crack penetrates the compression zone, and causes a diagonal tension failure. For short beams with a/d |
< 2.5, a shear-compression failure occurs.In performed numerical simulation four members corresponding to the tested beams were modeled. The numerical calculations were done using the commercial program ABAQUS 6.6, which is based on finite element method. Since the four-point test is symmetrical and beams were reinforced symmetrically by two longitudinal steel bars 18 mm in diameter, the three-dimensional (3D) FEM-analysis was performed on one quarter of the structure and appropriate boundary conditions were applied on the cuts (see ). In numerical simulations the linear elastic model was used. The FEM-beam was made by two components: concrete as a bulk material and steel bars as reinforcement. The connection between them was realized as a tie – the same displacements of connected nodes. Concrete was modeled by 8-node linear 3D brick elements (C3D8R) with reduced integration and hourglass control (number of brick elements 26,224) and steel bar was modeled by 2-node linear 3D truss elements (T3D2) (number of truss elements 51). Those elements were taken from the library of the ABAQUS program. While performing calculations, the same material properties for concrete and reinforcing steel as those obtained during the experiment were taken. To analyze the influence of the shear span-to-depth ratio on tensile stress distribution, four different shear spans (the distance between the support and applied force) were taken at modeling the member: a |
= 500; 550; 600 and 750 mm.As a result of FEM calculations, the dislocations of nodes and stress components along three axes of the global coordinate system were obtained. On the basis of the obtained results trajectories of σ11 stress were generated by the ABAQUS program. Next the results of calculations were compared. This comparison is presented in where there are presented the obtained numerical results for all beams when the applied force is P |
= 75 kN (V |
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